On optimal controls in coefficients for ill-posed elliptic Neumann boundary value problem with anisotropic p-Laplace operator
We study an optimal control problem for a nonlinear elliptic anisotropic p-Laplace equation with control constraints and Neumann boundary conditions. The matrix-valued coefficients Asym∈L∞(Ω;SsymN) we take as controls and in the linear part of differential operator we consider coefficients to be unb...
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| Published in | Nonlinear differential equations and applications Vol. 32; no. 3 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Springer Nature B.V
01.05.2025
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1021-9722 1420-9004 |
| DOI | 10.1007/s00030-025-01044-8 |
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| Abstract | We study an optimal control problem for a nonlinear elliptic anisotropic p-Laplace equation with control constraints and Neumann boundary conditions. The matrix-valued coefficients Asym∈L∞(Ω;SsymN) we take as controls and in the linear part of differential operator we consider coefficients to be unbounded skew-symmetric matrix Askew∈Lq(Ω;SskewN). We show that, in spite of unboundedness of the differential operator, the considered Neumann problem admits at least one weak solution and the corresponding OCP is well-possed and solvable. |
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| AbstractList | We study an optimal control problem for a nonlinear elliptic anisotropic p-Laplace equation with control constraints and Neumann boundary conditions. The matrix-valued coefficients Asym∈L∞(Ω;SsymN) we take as controls and in the linear part of differential operator we consider coefficients to be unbounded skew-symmetric matrix Askew∈Lq(Ω;SskewN). We show that, in spite of unboundedness of the differential operator, the considered Neumann problem admits at least one weak solution and the corresponding OCP is well-possed and solvable. |
| ArticleNumber | 46 |
| Author | Kogut, Peter Kupenko, Olha |
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| Cites_doi | 10.1007/978-3-642-87722-3 10.4171/zaa/1447 10.1007/BF02465783 10.1007/s11587-014-0202-z 10.1016/0021-8928(64)90165-0 10.1023/B:FAIA.0000042802.86050.5e 10.1016/j.crma.2009.05.008 10.1007/s10957-011-9840-4 10.3934/dcds.2014.34.2105 10.1007/978-0-8176-8149-4 10.3934/mcrf.2015.5.73 10.1007/s13163-010-0030-y 10.1007/978-3-0348-0513-1 10.1093/oso/9780198502456.001.0001 10.1006/jfan.1999.3556 10.1007/BF02505902 10.1016/j.anihpc.2009.04.005 10.1515/9783110668520 10.1137/100815761 |
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| SubjectTerms | Boundary conditions Boundary value problems Differential equations Laplace equation Laplace transforms Neumann problem Operators (mathematics) Optimal control |
| Title | On optimal controls in coefficients for ill-posed elliptic Neumann boundary value problem with anisotropic p-Laplace operator |
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