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.
Citation
Vy Khoi Le. "On second order elliptic equations and variational inequalities with anisotropic principal operators." Topol. Methods Nonlinear Anal. 44 (1) 41 - 72, 2014.
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