We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Inverse problems for anisotropic obstacle problems with multivalued convection and unbalanced growth.
- Authors
Zeng, Shengda; Bai, Yunru; Rădulescu, Vicenţiu D.
- Abstract
The prime goal of this paper is to introduce and study a highly nonlinear inverse problem of identification discontinuous parameters (in the domain) and boundary data in a nonlinear variable exponent elliptic obstacle problem involving a nonhomogeneous, nonlinear partial differential operator, which is formulated the sum of a weighted anisotropic $ p $-Laplacian and a weighted anisotropic $ q $-Laplacian (called the weighted anisotropic $ (p,q) $-Laplacian), a multivalued reaction term depending on the gradient, two multivalued boundary conditions and an obstacle constraint. We, first, employ the theory of nonsmooth analysis and a surjectivity theorem for pseudomonotone operators to prove the existence of a nontrivial solution of the anisotropic elliptic obstacle problem, which relies on the first eigenvalue of the Steklov eigenvalue problem for the $ p\_$-Laplacian. Then, we introduce the parameter-to-solution map for the anisotropic elliptic obstacle problem, and establish a critical convergence result of the Kuratowski type to parameter-to-solution map. Finally, a general framework is proposed to examine the solvability of the nonlinear inverse problem.
- Subjects
NONLINEAR partial differential operators; INVERSE problems; LAPLACIAN operator; MONOTONE operators; NONSMOOTH optimization; NONLINEAR equations
- Publication
Evolution Equations & Control Theory, 2023, Vol 12, Issue 3, p1
- ISSN
2163-2480
- Publication type
Article
- DOI
10.3934/eect.2022051