Data di Pubblicazione:
2009
Citazione:
Rigidity results for some boundary quasilinear phase transitions / Y. Sire, E. Valdinoci. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 34:7-9(2009), pp. 765-784. [10.1080/03605300902892402]
Abstract:
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Allen-Cahn phase transitions; Boundary reactions; Minimal surface operator; p-Laplacian; Poincare-type inequality; Quasilinear equations
Elenco autori:
Y. Sire, E. Valdinoci
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