No-flux boundary value problems with anisotropic variable exponents. (English) Zbl 1316.35109
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.
Reviewer: Dagmar Medková (Praha)
MSC:
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35D30 | Weak solutions to PDEs |
| 35J20 | Variational methods for second-order elliptic equations |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Keywords:
anisotropic variable exponents; Sobolev-type spaces; elliptic problems; no-flux boundary conditions; weak solutions; existence; uniqueness; multiplicityReferences:
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