Variational analysis of nonlocal Dirichlet problems in periodically perforated domains
In this paper we consider a family of non local functionals of convolution-type depending on a small parameter and -converging to local functionals defined on Sobolev spaces as . We study the asymptotic behaviour of the functionals when the order parameter is subject to Dirichlet conditions on a per...
Saved in:
| Published in | Calculus of variations and partial differential equations Vol. 64; no. 7; p. 232 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.09.2025
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0944-2669 1432-0835 |
| DOI | 10.1007/s00526-025-03071-w |
Cover
| Abstract | In this paper we consider a family of non local functionals of convolution-type depending on a small parameter
and
-converging to local functionals defined on Sobolev spaces as
. We study the asymptotic behaviour of the functionals when the order parameter is subject to Dirichlet conditions on a periodically perforated domains, given by a periodic array of small balls of radius
centered on a
–periodic lattice, being
an additional small parameter and
. We highlight differences and analogies with the local case, according to the interplay between the three scales
,
and
. A fundamental tool in our analysis turns out to be a non local variant of the classical Gagliardo–Nirenberg–Sobolev inequality in Sobolev spaces which may be of independent interest and useful for other applications. |
|---|---|
| AbstractList | In this paper we consider a family of non local functionals of convolution-type depending on a small parameter and -converging to local functionals defined on Sobolev spaces as . We study the asymptotic behaviour of the functionals when the order parameter is subject to Dirichlet conditions on a periodically perforated domains, given by a periodic array of small balls of radius centered on a –periodic lattice, being an additional small parameter and . We highlight differences and analogies with the local case, according to the interplay between the three scales , and . A fundamental tool in our analysis turns out to be a non local variant of the classical Gagliardo–Nirenberg–Sobolev inequality in Sobolev spaces which may be of independent interest and useful for other applications. In this paper we consider a family of non local functionals of convolution-type depending on a small parameter and -converging to local functionals defined on Sobolev spaces as . We study the asymptotic behaviour of the functionals when the order parameter is subject to Dirichlet conditions on a periodically perforated domains, given by a periodic array of small balls of radius centered on a –periodic lattice, being an additional small parameter and . We highlight differences and analogies with the local case, according to the interplay between the three scales , and . A fundamental tool in our analysis turns out to be a non local variant of the classical Gagliardo–Nirenberg–Sobolev inequality in Sobolev spaces which may be of independent interest and useful for other applications. |
| ArticleNumber | 232 |
| Author | Alicandro, Roberto Gelli, Maria Stella Leone, Chiara |
| Author_xml | – sequence: 1 givenname: Roberto surname: Alicandro fullname: Alicandro, Roberto organization: Dipartimento di Matematica “R. Caccioppoli”, Università di Napoli Federico II – sequence: 2 givenname: Maria Stella orcidid: 0000-0002-0932-7582 surname: Gelli fullname: Gelli, Maria Stella email: maria.stella.gelli@unipi.it organization: Dipartimento di Matematica, Università di Pisa – sequence: 3 givenname: Chiara surname: Leone fullname: Leone, Chiara organization: Dipartimento di Matematica “R. Caccioppoli”, Università di Napoli Federico II |
| BookMark | eNp9kEtLAzEQx4NUsK1-AU8LnqOT1z6OUrUKBS_aa8hrNWW7qcmW0m9v6grevMwww_8_j98MTfrQO4SuCdwSgOouAQhaYqACA4OK4MMZmhLOKIaaiQmaQsM5pmXZXKBZShsAImrKp2i9VtGrwYdedYXK4Zh8KkJb5AVdMLn54KM3n50bil0MunPbVPi-2Lnog_VZ0B1PRRuiGpwtbNgq36dLdN6qLrmr3zxH70-Pb4tnvHpdvizuV9jQig6YUdbWmhnrrNUlcNCaEC2Aclu3BFSlmCJWi9Jq5XTNKeOmMQbAAClF5dgc3Yxz821fe5cGuQn7mN9IklEhamiaqs4qOqpMDClF18pd9FsVj5KAPPGTIz-Z-ckffvKQTWw0pSzuP1z8G_2P6xvUoncN |
| Cites_doi | 10.3934/nhm.2008.3.523 10.1017/S0956792598003453 10.1016/j.matpur.2004.11.005 10.1137/23M1563438 10.1016/S0022-5096(99)00029-0 10.1016/j.anihpc.2012.01.006 10.1016/j.aim.2010.06.014 10.1088/0951-7715/28/11/3999 10.1007/s40818-018-0044-1 10.1137/S0036141003426471 10.1137/070698592 10.1007/s00440-024-01320-1 10.1007/978-981-99-0685-7 10.1016/S0021-7824(01)01226-0 10.1017/prm.2018.130 10.3934/nhm.2012.7.543 10.1007/s00526-003-0195-z 10.1007/s00526-015-0839-9 10.1007/BF02198476 10.1016/j.jfa.2011.11.005 10.1007/978-1-4612-0327-8 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. – notice: The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025. |
| DBID | AAYXX CITATION JQ2 |
| DOI | 10.1007/s00526-025-03071-w |
| DatabaseName | CrossRef ProQuest Computer Science Collection |
| DatabaseTitle | CrossRef ProQuest Computer Science Collection |
| DatabaseTitleList | ProQuest Computer Science Collection |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1432-0835 |
| ExternalDocumentID | 10_1007_s00526_025_03071_w |
| GrantInformation_xml | – fundername: Ministero dell’Istruzione, dell’Università e della Ricerca grantid: PRIN project 2022J4FYNJ; PRIN Project 2022E9CF89; PRIN PNRR Project P2022WJW9H funderid: http://dx.doi.org/10.13039/501100003407 – fundername: Deutsche Forschungsgemeinschaft grantid: EXC - 2047/1 - 390685813 funderid: http://dx.doi.org/10.13039/501100001659 – fundername: Ministero dell’Istruzione, dell’Università e della Ricerca grantid: PRIN Project 2022E9CF89 funderid: http://dx.doi.org/10.13039/501100003407 |
| GroupedDBID | -~C -~X .86 .VR 06D 0R~ 0VY 1N0 203 23N 2J2 2JN 2JY 2KG 2KM 2LR 2~H 30V 4.4 406 408 409 40D 40E 5GY 5VS 67Z 6NX 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAPKM AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYZH ABAKF ABBBX ABBRH ABBXA ABDBE ABDZT ABECU ABFSG ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABRTQ ABSXP ABTEG ABTHY ABTKH ABTMW ABWNU ABXPI ACAOD ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACSTC ACZOJ ADHHG ADHIR ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AEZWR AFBBN AFDZB AFHIU AFLOW AFOHR AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHSBF AHWEU AHYZX AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG ATHPR AVWKF AXYYD AYFIA AYJHY AZFZN B-. BA0 BAPOH BSONS CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI ESBYG F5P FEDTE FERAY FFXSO FIGPU FNLPD FRRFC FWDCC GGCAI GGRSB GJIRD GNWQR GQ7 GQ8 GXS HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV LAS LLZTM MA- N9A NB0 NPVJJ NQJWS O93 O9G O9I O9J OAM P19 P2P P9R PF0 PQQKQ PT4 PT5 QOK QOS R89 R9I RHV RNS ROL RPX RSV S16 S1Z S27 S3B SAP SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX VC2 W23 W48 WK8 YLTOR Z45 ZMTXR ~EX -Y2 1SB 2.D 28- 2P1 2VQ 5QI 88I AARHV AAYTO AAYXX ABJCF ABQSL ABULA ACBXY ADHKG AEBTG AEFIE AEKMD AFEXP AFGCZ AGGDS AGQPQ AJBLW AMVHM BBWZM BDATZ BGLVJ BGNMA CAG CCPQU CITATION COF EJD FINBP FSGXE H13 K7- KOW M2P M4Y M7S N2Q NDZJH NU0 O9- PHGZM PHGZT PQGLB PTHSS Q2X R4E RNI RZK S26 S28 SCLPG T16 UZXMN VFIZW ZWQNP JQ2 |
| ID | FETCH-LOGICAL-c272t-323f8b3cdeddb6040bb11b5024d8f10a7a3a1db56dbaeb84234c9cc00c01657e3 |
| IEDL.DBID | U2A |
| ISSN | 0944-2669 |
| IngestDate | Wed Oct 01 06:55:56 EDT 2025 Wed Oct 01 05:26:48 EDT 2025 Sun Aug 24 01:10:46 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 7 |
| Keywords | 49J45 49J55 35B27 35B40 74Q05 45E10 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c272t-323f8b3cdeddb6040bb11b5024d8f10a7a3a1db56dbaeb84234c9cc00c01657e3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-0932-7582 |
| PQID | 3255809978 |
| PQPubID | 32028 |
| ParticipantIDs | proquest_journals_3255809978 crossref_primary_10_1007_s00526_025_03071_w springer_journals_10_1007_s00526_025_03071_w |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2025-09-01 |
| PublicationDateYYYYMMDD | 2025-09-01 |
| PublicationDate_xml | – month: 09 year: 2025 text: 2025-09-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Heidelberg |
| PublicationTitle | Calculus of variations and partial differential equations |
| PublicationTitleAbbrev | Calc. Var |
| PublicationYear | 2025 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V |
| References | T Mengesha (3071_CR20) 2015; 28 N Ansini (3071_CR5) 2002; 81 R Alicandro (3071_CR3) 2004; 36 MC Pereira (3071_CR21) 2020; 150 R Alicandro (3071_CR4) 2000; 29 M Focardi (3071_CR17) 2010; 225 3071_CR13 JC Bellido (3071_CR7) 2015; 54 J Heinonen (3071_CR19) 1993 AC Ponce (3071_CR22) 2004; 19 G Alberti (3071_CR1) 1998; 9 SA Silling (3071_CR27) 2000; 48 L Caffarelli (3071_CR12) 2008; 3 3071_CR6 L Sigalotti (3071_CR26) 2008; 15 L Sigalotti (3071_CR25) 2012; 7 R Alicandro (3071_CR2) 2023 D Finkelshtein (3071_CR16) 2012; 262 G Dal Maso (3071_CR14) 1993 3071_CR24 J Bourgain (3071_CR8) 2001 G Gilboa (3071_CR18) 2008; 7 3071_CR28 H Brezis (3071_CR11) 2018; 4 O Savin (3071_CR23) 2012; 29 A Braides (3071_CR10) 1996; 135 A Braides (3071_CR9) 2002 LC Evans (3071_CR15) 1992 |
| References_xml | – volume: 3 start-page: 523 year: 2008 ident: 3071_CR12 publication-title: Netw. Heterog. Media doi: 10.3934/nhm.2008.3.523 – volume: 9 start-page: 261 year: 1998 ident: 3071_CR1 publication-title: Eur. J. Appl. Math. doi: 10.1017/S0956792598003453 – ident: 3071_CR6 doi: 10.1016/j.matpur.2004.11.005 – volume-title: Measure Theory and Fine Properties of Funtions year: 1992 ident: 3071_CR15 – volume: 15 start-page: 655 year: 2008 ident: 3071_CR26 publication-title: J. Convex Anal. – ident: 3071_CR28 doi: 10.1137/23M1563438 – volume-title: Nonlinear Potential Theory of Degenerate Elliptic Equations year: 1993 ident: 3071_CR19 – volume: 48 start-page: 175 year: 2000 ident: 3071_CR27 publication-title: J. Mech. Phys. Solids doi: 10.1016/S0022-5096(99)00029-0 – ident: 3071_CR13 – volume: 29 start-page: 479 year: 2012 ident: 3071_CR23 publication-title: Ann. Inst. H. Poincaré Anal. Non Linéaire doi: 10.1016/j.anihpc.2012.01.006 – volume: 225 start-page: 3502 year: 2010 ident: 3071_CR17 publication-title: Adv. Math. doi: 10.1016/j.aim.2010.06.014 – volume-title: -Convergence for Beginners, Oxford Lecture Series in Mathematics and Its Applications$$\Gamma $$ year: 2002 ident: 3071_CR9 – volume: 28 start-page: 3999 year: 2015 ident: 3071_CR20 publication-title: Nonlinearity doi: 10.1088/0951-7715/28/11/3999 – start-page: 439 volume-title: Another Look at Sobolev Spaces, Optimal Control and Partial Differential Equations year: 2001 ident: 3071_CR8 – volume: 4 start-page: 1 year: 2018 ident: 3071_CR11 publication-title: Ann. PDE doi: 10.1007/s40818-018-0044-1 – volume: 36 start-page: 1 year: 2004 ident: 3071_CR3 publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141003426471 – volume: 7 start-page: 1005 year: 2008 ident: 3071_CR18 publication-title: Multiscale Model. Simul. doi: 10.1137/070698592 – ident: 3071_CR24 doi: 10.1007/s00440-024-01320-1 – volume-title: A Variational Theory of Convolution-type Functionals. SpringerBriefs on PDEs and Data Science year: 2023 ident: 3071_CR2 doi: 10.1007/978-981-99-0685-7 – volume: 81 start-page: 439 year: 2002 ident: 3071_CR5 publication-title: J. Math. Pures Appl. doi: 10.1016/S0021-7824(01)01226-0 – volume: 150 start-page: 305 year: 2020 ident: 3071_CR21 publication-title: Proc. R. Soc. Edinb. doi: 10.1017/prm.2018.130 – volume: 7 start-page: 543 year: 2012 ident: 3071_CR25 publication-title: Netw. Heterog. Media doi: 10.3934/nhm.2012.7.543 – volume: 19 start-page: 229 year: 2004 ident: 3071_CR22 publication-title: Calc. Var. Partial. Differ. Equ. doi: 10.1007/s00526-003-0195-z – volume: 54 start-page: 1643 year: 2015 ident: 3071_CR7 publication-title: Calc. Var. Partial. Differ. Equ. doi: 10.1007/s00526-015-0839-9 – volume: 135 start-page: 297 year: 1996 ident: 3071_CR10 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/BF02198476 – volume: 262 start-page: 1274 year: 2012 ident: 3071_CR16 publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2011.11.005 – volume: 29 start-page: 671 year: 2000 ident: 3071_CR4 publication-title: Ann. Scuola Norm. Sup. Pisa Cl. Sci. – volume-title: An Introduction to $$\Gamma $$-Convergence year: 1993 ident: 3071_CR14 doi: 10.1007/978-1-4612-0327-8 |
| SSID | ssj0015824 |
| Score | 2.4021366 |
| Snippet | In this paper we consider a family of non local functionals of convolution-type depending on a small parameter
and
-converging to local functionals defined on... In this paper we consider a family of non local functionals of convolution-type depending on a small parameter and -converging to local functionals defined on... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 232 |
| SubjectTerms | Analysis Asymptotic properties Calculus of Variations and Optimal Control; Optimization Control Convergence Dirichlet problem Homogenization Mathematical and Computational Physics Mathematics Mathematics and Statistics Order parameters Sobolev space Systems Theory Theoretical |
| Title | Variational analysis of nonlocal Dirichlet problems in periodically perforated domains |
| URI | https://link.springer.com/article/10.1007/s00526-025-03071-w https://www.proquest.com/docview/3255809978 |
| Volume | 64 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVLSH databaseName: SpringerLink Journals customDbUrl: mediaType: online eissn: 1432-0835 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0015824 issn: 0944-2669 databaseCode: AFBBN dateStart: 19930301 isFulltext: true providerName: Library Specific Holdings – providerCode: PRVAVX databaseName: SpringerLINK - Czech Republic Consortium customDbUrl: eissn: 1432-0835 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0015824 issn: 0944-2669 databaseCode: AGYKE dateStart: 19970101 isFulltext: true titleUrlDefault: http://link.springer.com providerName: Springer Nature – providerCode: PRVAVX databaseName: SpringerLink Journals (ICM) customDbUrl: eissn: 1432-0835 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0015824 issn: 0944-2669 databaseCode: U2A dateStart: 19970101 isFulltext: true titleUrlDefault: http://www.springerlink.com/journals/ providerName: Springer Nature |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDI5gu8AB8RSDMeXADSK1TR_ZcUIbE2ic2DROVRKnYhJsiA5N_HucLO0EggPHqpUVfbFju44_E3IJUovQAGdBVkQslmHKZAGKaRApQFDE2k0tGT2kw3F8N02mvimsrG67VyVJd1LXzW6OmoTZ8atWMUO22ibNxNJ5oRaPo15dO0iEG2WLeUvM0P10favM7zK-u6NNjPmjLOq8zWCf7PkwkfbW-3pAtsz8kOyOao7V8ohMJpjm-l95VHpuEbooKCb0zkNRPM5m-hk3hvqxMSWdzamlNl646szLp30orBIYoLB4lbN5eUzGg_7jzZD5KQlMR1m0ZDzihVBcgwFQKdqkUmGoEvS9IIowkJnkMgSVpKCkUQLDp1h3tQ4CbTuZMsNPSAMXZk4JTSSPZACZtOV4FWMmgfYvUgUyDrsgRYtcVWDlb2syjLymPXbQ5ght7qDNVy3SrvDMvWGUOccURthuXRR2XWG8ef23tLP_fX5OdiK3zfY2WJs0lu8f5gLDh6XqkGbv9um-33Fa8wU0A7_4 |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LTwIxEG4UD-rB-Iwoag_etMl2u49yJEaCCpyAcGvaTjeSKBgXQ_z3tqUL0ejB42Y3k-abTmdmp_MNQtcgNacGGInyIiaJpBmRBSiigWcAUZFoP7Wk1886w-RxnI5DU1hZ3XavSpL-pF41u3lqEuLGr7qNScliE205AivHmD-MW6vaQcr9KFubtyTEup9maJX5XcZ3d7SOMX-URb23ae-jvRAm4tZSrwdow0wP0W5vxbFaHqHRyKa54VceloFbBM8KbBN676GwPc4m-tkqBoexMSWeTLGjNp756szLp3so3CYwgGH2KifT8hgN2_eDuw4JUxKIjvN4TljMCq6YBgOgMmuTSlGqUut7gRc0krlkkoJKM1DSKG7Dp0Q3tY4i7TqZcsNOUM0uzJwinEoWywhy6crxKrGZhLV_nimQCW2C5HV0U4El3pZkGGJFe-yhFRZa4aEVizpqVHiKYBilYDaF4a5b1wq7rTBev_5b2tn_Pr9C251Bryu6D_2nc7QTe5W7m2ENVJu_f5gLG0rM1aXfOV9MUsFQ |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDI5gSAgOiKcYDMiBG0Tru9lxAqbx2MSBTbtFSdyKSdBNtGji3-NkXQcIDhyrVlZkO7Fd5_tMyDlIzd0EfObEqccC6UZMpqCYBh4BOGmg7dSSXj_qDoK7UTj6guK3t90XLck5psGwNGVFcwppswK-WZoSZkaxGid12WyVrAWGKAE9euC1qz5CyO1YW6xhAoahqFXCZn6X8T00LfPNHy1SG3k622SrTBlpe27jHbKSZLtks1fxreZ7ZDjEkrf8rUdlyTNCJynF4t5GK4pH21g_o5FoOUImp-OMGprjie3UvHyYh9Q4RAIUJq9ynOX7ZNC5ebrqsnJiAtNe7BXM9_yUK19DAqAi3J9Kua4KMQ4DT11HxtKXLqgwAiUTxTGVCnRLa8fRBtUUJ_4BqeHCkkNCQ-l70oFYmta8CrCqwLOARwpk4LZA8jq5WChLTOfEGKKiQLaqFahaYVUrZnXSWOhTlJskFz6WM9wgd1HY5ULHy9d_Szv63-dnZP3xuiMebvv3x2TDsxY3l8QapFa8vScnmFUU6tQ6zies1cWM |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Variational+analysis+of+nonlocal+Dirichlet+problems+in+periodically+perforated+domains&rft.jtitle=Calculus+of+variations+and+partial+differential+equations&rft.au=Alicandro%2C+Roberto&rft.au=Gelli%2C+Maria+Stella&rft.au=Leone%2C+Chiara&rft.date=2025-09-01&rft.pub=Springer+Berlin+Heidelberg&rft.issn=0944-2669&rft.eissn=1432-0835&rft.volume=64&rft.issue=7&rft_id=info:doi/10.1007%2Fs00526-025-03071-w&rft.externalDocID=10_1007_s00526_025_03071_w |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0944-2669&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0944-2669&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0944-2669&client=summon |