Maximal solutions for $-\Delta u+u^q=0$ in open or finely open sets

Abstract : We study the existence and uniqueness of new classes of solutions of the superlinear equation $-\Delta u+u^q=0$ (q>1) in a domain of R^N or in a finely open set for the topology associated to the Bessel capacity C_{2,q'}. Condition of existence or uniqueness of solutions with boundary blow-up are obtained generalizing the results of Dhersin-Le Gall and of Labutin.
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Submitted on : Friday, December 19, 2008 - 3:27:41 PM
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  • HAL Id : hal-00328094, version 3
  • ARXIV : 0810.1667

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Moshe Marcus, Laurent Veron. Maximal solutions for $-\Delta u+u^q=0$ in open or finely open sets. Journal de Mathématiques Pures et Appliquées, Elsevier, 2009. ⟨hal-00328094v3⟩

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