Szczegóły publikacji

Opis bibliograficzny

Autorzy (3)

• Zeng Shengda
• Bai Yunru
• AGHRǎdulescu Vicenţiu

Słowa kluczowe

Dane bibliometryczne

ID BaDAP	146495
Data dodania do BaDAP	2023-05-16
Tekst źródłowy	URL
DOI	10.3934/eect.2022051
Rok publikacji	2023
Typ publikacji	artykuł w czasopiśmie
Otwarty dostęp
Creative Commons
Czasopismo/seria	Evolution Equations and Control Theory

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 -Laplacian and a weighted anisotropic -Laplacian (called the weighted anisotropic -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 -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.

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