On the improved interior regularity of the solution of a fourth order elliptic problem modelling the displacement of a linearly elastic shallow shell lying subject to an obstacle
In this paper we show that the solution of an obstacle problem for linearly elastic shallow shells enjoys higher differentiability properties in the interior of the domain where it is defined.
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| Published in | Asymptotic analysis Vol. 127; no. 1-2; pp. 35 - 55 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
London, England
SAGE Publications
01.01.2022
Sage Publications Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0921-7134 1875-8576 |
| DOI | 10.3233/ASY-211672 |
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| Abstract | In this paper we show that the solution of an obstacle problem for linearly elastic shallow shells enjoys higher differentiability properties in the interior of the domain where it is defined. |
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| AbstractList | In this paper we show that the solution of an obstacle problem for linearly elastic shallow shells enjoys higher differentiability properties in the interior of the domain where it is defined. |
| Author | Piersanti, Paolo |
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| Copyright | 2022 – IOS Press. All rights reserved. Copyright IOS Press BV 2021 |
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| Keywords | obstacle problems improved regularity elliptic variational inequalities Shallow shell fourth order problems |
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| References | 2018; 131 2010; 98 1973; 9 2020; 85 2019; 24 2018; 356 1971; 36 1979; 6 2019; 357 1955; 8 1982; 103 1972; 45 1992; 45 2018; 97 2008; 90 ref009 ref007 ref018 ref008 ref019 ref005 ref016 ref006 ref017 ref003 ref014 ref004 ref015 ref012 ref002 ref013 ref010 ref021 ref011 ref022 Caffarelli L.A. (ref001) 1979; 6 ref020 |
| References_xml | – volume: 103 start-page: 325 year: 1982 end-page: 335 article-title: The two-obstacle problem for the biharmonic operator publication-title: Pacific J. Math. – volume: 24 start-page: 1503 issue: 5 year: 2019 end-page: 1529 article-title: An obstacle problem for elliptic membrane shells publication-title: Math. Mech. Solids – volume: 98 start-page: 115 year: 2010 end-page: 116 article-title: Erratum to: Mathematical justification of the obstacle problem in the case of a shallow shell publication-title: J. Elasticity – volume: 45 start-page: 327 issue: 3 year: 1992 end-page: 360 article-title: Justification of the two-dimensional equations of a linearly elastic shallow shell publication-title: Comm. Pure Appl. Math. – volume: 6 start-page: 151 year: 1979 end-page: 184 article-title: The obstacle problem for the biharmonic operator publication-title: Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) – volume: 131 start-page: 19 year: 2018 end-page: 38 article-title: A linearly elastic shell over an obstacle: The flexural case publication-title: J. Elasticity – volume: 357 start-page: 221 year: 2019 end-page: 230 article-title: A confinement problem for a linearly elastic Koiter’s shell publication-title: C.R. Acad. Sci. Paris, Sér. I – volume: 9 start-page: 91 year: 1973 end-page: 103 article-title: On the regularity of the solution of the biharmonic variational inequality publication-title: Manuscripta Math. – volume: 45 start-page: 294 year: 1972 end-page: 320 article-title: Absolute continuity on tracks and mappings of Sobolev spaces publication-title: Arch. Rational Mech. Anal. – volume: 90 start-page: 241 year: 2008 end-page: 257 article-title: Mathematical justification of the obstacle problem in the case of a shallow shell publication-title: J. Elasticity – volume: 85 start-page: 623 year: 2020 end-page: 652 article-title: Numerical methods for static shallow shells lying over an obstacle publication-title: Numer. Algorithms – volume: 356 start-page: 1040 issue: 10 year: 2018 end-page: 1051 article-title: Un problème de confinement pour une coque membranaire linéairement élastique de type elliptique publication-title: C. R. Math. Acad. Sci. Paris – volume: 24 start-page: 3061 year: 2019 end-page: 3079 article-title: Obstacle problems for Koiter’s shells publication-title: Math. Mech. Solids – volume: 97 start-page: 1261 year: 2018 end-page: 1280 article-title: Mathematical justification of the obstacle problem for elastic elliptic membrane shells publication-title: Applicable Anal. – volume: 36 start-page: 140 year: 1971 end-page: 149 article-title: Zum Differenzierbarkeitsproblem bei Variationsungleichungen höherer Ordnung publication-title: Abh. Math. Sem. Univ. Hamburg – volume: 8 start-page: 649 year: 1955 end-page: 675 article-title: Remarks on strongly elliptic partial differential equations publication-title: Comm. Pure Appl. Math. – ident: ref006 – ident: ref005 – ident: ref003 – ident: ref004 – ident: ref020 doi: 10.1002/cpa.3160080414 – ident: ref015 doi: 10.1007/BF01320669 – ident: ref016 doi: 10.1007/s10659-007-9141-1 – ident: ref019 doi: 10.1007/BF00251378 – ident: ref009 doi: 10.1177/1081286518800164 – ident: ref010 doi: 10.1002/cpa.3160450305 – ident: ref022 doi: 10.1080/00036811.2017.1337894 – ident: ref008 doi: 10.1016/j.crma.2018.08.002 – ident: ref017 doi: 10.1007/s10659-009-9230-4 – ident: ref002 doi: 10.2140/pjm.1982.103.325 – ident: ref021 doi: 10.1007/s11075-019-00830-7 – ident: ref011 doi: 10.1016/j.crma.2019.01.004 – ident: ref018 doi: 10.1007/s10659-017-9643-4 – ident: ref012 doi: 10.1177/1081286519825979 – ident: ref013 – ident: ref014 doi: 10.1007/BF02995917 – ident: ref007 doi: 10.1137/1.9781611972597 – volume: 6 start-page: 151 year: 1979 ident: ref001 publication-title: Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) |
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| Title | On the improved interior regularity of the solution of a fourth order elliptic problem modelling the displacement of a linearly elastic shallow shell lying subject to an obstacle |
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