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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Bibliographic Details
Published inNonlinear differential equations and applications Vol. 32; no. 3
Main Authors Kogut, Peter, Kupenko, Olha
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.05.2025
Subjects
Boundary conditions
Boundary value problems
Differential equations
Laplace equation
Laplace transforms
Neumann problem
Operators (mathematics)
Optimal control
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Summary: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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ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-025-01044-8