Existence of solutions for unilateral problems associated to some quasilinear anisotropic elliptic equations with measure data

In this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type where is a Leray-Lions operator, the Carathéodory function , , ) is a nonlinear lower order term that verify some natural growth and sign conditions, where the data = − div belongs to...

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Published inNonautonomous Dynamical Systems Vol. 9; no. 1; pp. 68 - 90
Main Authors Al-Hawmi, Mohammed, Hjiaj, Hassane
Format Journal Article
LanguageEnglish
Published De Gruyter 01.01.2022
Subjects
35J15
35J62
anisotropic Sobolev spaces
entropy solutions
measure data
nonlinear elliptic equations
Unilateral problem
Online AccessGet full text
ISSN2353-0626
2353-0626
DOI10.1515/msds-2022-0147

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Abstract In this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type where is a Leray-Lions operator, the Carathéodory function , , ) is a nonlinear lower order term that verify some natural growth and sign conditions, where the data = − div belongs to −dual and (·) ∈ , ).
AbstractList In this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type where is a Leray-Lions operator, the Carathéodory function , , ) is a nonlinear lower order term that verify some natural growth and sign conditions, where the data = − div belongs to −dual and (·) ∈ , ).
In this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type {Au+g(x,u,∇u)=μ−div φ(u)in Ω,u=0on  ∂Ω,\left\{ {\matrix{{Au + g\left( {x,u,\nabla u} \right) = \mu - div\,\phi \left( u \right)} \hfill & {in\,\Omega ,} \hfill \cr {u = 0} \hfill & {on\,\,\partial \Omega ,} \hfill \cr } } \right. where Au=−∑i=1N∂∂xiai(x,u,∇u)Au = - \sum\limits_{i = 1}^N {{\partial \over {\partial {x_i}}}{a_i}\left( {x,u,\nabla u} \right)} is a Leray-Lions operator, the Carathéodory function g(x, s, ξ) is a nonlinear lower order term that verify some natural growth and sign conditions, where the data µ = f − div F belongs to L1−dual and ϕ (·) ∈ C0(R, RN).
In this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type { A u + g ( x , u , ∇ u ) = μ − d i v   φ ( u ) i n   Ω , u = 0 o n     ∂ Ω , \left\{ {\matrix{{Au + g\left( {x,u,\nabla u} \right) = \mu - div\,\phi \left( u \right)} \hfill & {in\,\Omega ,} \hfill \cr {u = 0} \hfill & {on\,\,\partial \Omega ,} \hfill \cr } } \right. where A u = − ∑ i = 1 N ∂ ∂ x i a i ( x , u , ∇ u ) Au = - \sum\limits_{i = 1}^N {{\partial \over {\partial {x_i}}}{a_i}\left( {x,u,\nabla u} \right)} is a Leray-Lions operator, the Carathéodory function g ( x , s , ξ ) is a nonlinear lower order term that verify some natural growth and sign conditions, where the data µ = f − div F belongs to L 1 −dual and ϕ (·) ∈ C 0 ( R , R N ).
Author Hjiaj, Hassane
Al-Hawmi, Mohammed
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Snippet In this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type where is a Leray-Lions operator, the...
In this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type { A u + g ( x , u , ∇ u ) = μ − d i v   φ...
In this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type {Au+g(x,u,∇u)=μ−div φ(u)in Ω,u=0on ...
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SubjectTerms 35J15
35J62
anisotropic Sobolev spaces
entropy solutions
measure data
nonlinear elliptic equations
Unilateral problem
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Title Existence of solutions for unilateral problems associated to some quasilinear anisotropic elliptic equations with measure data
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