No-flux boundary value problems with anisotropic variable exponents (Q2339861)

Let \(\Omega \subset\mathbb R^N\) be a rectangular-like domain. The paper studies the nonlinear elliptic problem \(-\sum_{i=1}^N \partial_i a_i (x,\partial_i u)+b(x)|u|^{p(x)-2}u=\lambda f(x,u)\) in \(\Omega \), \(u\equiv\mathrm{constant}\) on \(\partial \Omega \), \(\int_{\partial \Omega }\sum_{i=1}^N a_i(x,\partial_i u)\nu_i \;{\mathrm d}S=0\) in anisotropic variable exponent Sobolev spaces.