L1 Existence and Uniqueness of Entropy Solutions to Nonlinear Multivalued Elliptic Equations with Homogeneous Neumann Boundary Condition and Variable Exponent

Authors

Stanislas\u0003 Ouaro Universit\u00e9 Ouaga I Pr Joseph KI-ZERBO, LAboratoire de Math\u00e9matique et Informatique (LAMI), Unit\u00e9 de Formation et de Recherches en Sciences Exactes et Appliqu\u00e9es, D\u00e9partement de Math\u00e9matiques, 03 BP 7021 Ouaga 03 Ouagadougou, Burkina Faso
Arouna Ouedraogo Universit\u00e9 de Ouagadougou, Unit\u00e9 de Formation et de Recherche en Sciences Exactes et Appliqu\u00e9es, D\u00e9partement de Math\u00e9matiques B.P.7021 Ouagadougou 03, Burkina Faso

DOI:

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

Keywords:

Elliptic equation;variable exponent;entropy solution;L¹-data;Neumann boundary condition

Abstract

In this work, we study the following nonlinear homogeneous Neumann boundary value problem $\u03b2(u)\u2212diva(x,\u2207u) \u220b f in \u03a9, a(x,\u2207u)\u22c5\u03b7$ $=0$ on $\u2202\u03a9$, where $\u03a9$ is a smooth bounded open domain in $\u211c^N, N \u2265 3$ with smooth boundary $\u2202\u03a9$ and $\u03b7$ the outer unit normal vector on $\u2202\u03a9$. We prove the existence and uniqueness of an entropy solution for L\u00b9-data f. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.<\/p>"

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Published

2014-03-05

Issue

Vol. 27 No. 1 (2014)

Section

Articles