Liouville theorem on a half-space for biharmonic problem with Dirichlet boundary condition

Autor:	Mtiri, Foued, Selmi, Abdelbaki, Zaid, Cherif
Rok vydání:	2021
Předmět:	Mathematics - Analysis of PDEs Mathematics - Classical Analysis and ODEs
Druh dokumentu:	Working Paper
Popis:	We investigate here the nonlinear elliptic H\'enon type equation: $$\D^{2} u= |x|^a|u|^{p-1}u \; \,\,\mbox{in}\,\,\,\, \R^{n}_{+}, \quad \quad u =\frac{\partial u}{\partial x_n} = 0 \quad \mbox{in}\,\,\,\, \partial \R^{n}_{+},$$ with $p>1$ and $n\geq 2$. In particular, we prove some Liouville type theorems for stable at infinity solutions. The main methods used are the integral estimates, the Pohozaev-type identity and the monotonicity formula.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2107.04995 Zobrazit plný text záznamu View this record from Arxiv