Séminaire d'Analyse
Large solution to elliptic equations involving fractional LaplacianHuyuan CHEN (Université du Chili, Santiago)
Thursday 29 November 2012 11:00 - Tours - Salle 1180 (Bât E2)
Résumé :
We consider the large solution of \begin{equation} \left\{ \begin{array}{lll} (-\Delta)^{\alpha} u(x)+|u|^{p-1}u(x)=0,\ \ \ \ & x\in\Omega,\\[2mm] u(x)=0,& x\in\R^N\setminus\bar\Omega,\\[2mm] \lim_{x\in\Omega,\ x\to\partial\Omega}u(x)=+\infty, \end{array} \right. \end{equation} where $\Omega$ is an open, connected and bounded subset of $\mathbb{R}^N(N\ge2)$ with $C^2$ boundary $\partial \Omega$ and the fractional Laplacian operator may be defined as: $$ (-\Delta)^\alpha u(x):=-\frac12 \int_{\R^N}\frac{\delta(u,x,y)}{|y|^{N+2\alpha}}dy,\ \ x\in \Omega, $$ with $\alpha\in(0,1)$ and $\delta(u,x,y):=u(x+y)+u(x-y)-2u(x)$. In this note, we are interested in understanding how the non-local character influences the large solution of the equation and what is the structure of the large solution of the equation.
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