## Topological Methods in Nonlinear Analysis

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

Vy Khoi Le

#### 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

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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