Topological Methods in Nonlinear Analysis

On second order elliptic equations and variational inequalities with anisotropic principal operators

Vy Khoi Le

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Abstract

This paper is about boundary value problems of the form \begin{equation*} \begin{cases} -{\rm div} [\nabla \Phi(\nabla u)] = f(x,u) &\mbox{in } \Omega, \\ u=0 &\mbox{on } \partial\Omega, \end{cases} \end{equation*} where $\Phi$ is a convex function of $\xi\in \mathbb{R}^N$, rather than a function of the norm $|\xi|$. The problem is formulated appropriately in an anisotropic Orlicz-Sobolev space associated with $\Phi$. We study the existence of solutions and some other properties of the above problem and its corresponding variational inequality in such space.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 44, Number 1 (2014), 41-72.

Dates
First available in Project Euclid: 11 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1460381469

Mathematical Reviews number (MathSciNet)
MR3289007

Zentralblatt MATH identifier
1376.35050

Citation

Le, Vy Khoi. On second order elliptic equations and variational inequalities with anisotropic principal operators. Topol. Methods Nonlinear Anal. 44 (2014), no. 1, 41--72. https://projecteuclid.org/euclid.tmna/1460381469


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