Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 34, Issue 7, Pages 765-784Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605300902892402
Keywords
Allen-Cahn phase transitions; Boundary reactions; Minimal surface operator; p-Laplacian; Poincare-type inequality; Quasilinear equations
Categories
Funding
- MIUR Metodi Variazionali Ed Equazioni Differenziali Nonlineari
- FIRB Analysis and Beyond
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We consider a quasilinear equation given in the half-space, i.e., a so called boundary reaction problem. Our concerns are a geometric Poincare inequality and, as a byproduct of this inequality, a result on the symmetry of low-dimensional bounded stable solutions, under some suitable assumptions on the nonlinearities. More precisely, we analyze the following boundary problem [image omitted] under some natural assumptions on the diffusion coefficient a(x, |delta u|) and the nonlinearities f and g. Here, u=u(y,x), with yn and x(0, +). This type of PDE can be seen as a nonlocal problem on the boundary [image omitted]. The assumptions on a(x,|delta u|) allow to treat in a unified way the p-Laplacian and the minimal surface operators.
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