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 details Title Semi-stable and extremal solutions of reaction equations involving the p-Laplacian AbstractWe consider nonnegative solutions of $-\Delta_p u=f(x,u)$, where $p>1$ and $\Delta_p$ is the $p$-Laplace operator, in a smooth bounded domain of $\mathbb{R}^N$ with zero Dirichlet boundary conditions. We introduce the notion of semi-stability for a solution $u$, and we give examples and properties of this class of solutions. Under some assumptions on $f$ that make its growth comparable to $u^m$, we prove that every semi-stable solution is bounded if $m We also study a type of semi-stable solutions called extremal solutions, for which we establish optimal$L^\infty\$ estimates. Speaker(s) Manuel Sanchón (CMUC/Univ. Coimbra) Date November 25, 2005Time14.30 Room 5.5 CMUC Apartado 3008, 3001 - 454 Coimbra, Portugal T:+351 239 791 150 F:+351 239 793 069 cmuc@mat.uc.pt - developed by Flor de Utopia