<em>L</em><sup>1</sup> Existence and Uniqueness of Entropy Solutions to Nonlinear Multivalued Elliptic Equations with Homogeneous Neumann Boundary Condition and Variable Exponent

<em>L</em><sup>1</sup> Existence and Uniqueness of Entropy Solutions to Nonlinear Multivalued Elliptic Equations with Homogeneous Neumann Boundary Condition and Variable Exponent

Year:    2014

Author:    Stanislas Ouaro, Arouna Ouedraogo

Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 1 : pp. 1–27

Abstract

In this work, we study the following nonlinear homogeneous Neumann boundary value problem $β(u)−diva(x,∇u) ∋ f in Ω, a(x,∇u)⋅η$ $=0$ on $∂Ω$, where $Ω$ is a smooth bounded open domain in $ℜ^N, N ≥ 3$ with smooth boundary $∂Ω$ and $η$ the outer unit normal vector on $∂Ω$. We prove the existence and uniqueness of an entropy solution for L¹-data f. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v27.n1.1

Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 1 : pp. 1–27

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Elliptic equation

Author Details

Stanislas Ouaro

Arouna Ouedraogo