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Isolated boundary singularities of semilinear elliptic equations

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Ponce, Augusto [UCL] Véron, Laurent [Université François Rabelais] Bidaut-Véron, Marie-Françoise [Université François Rabelais]

Given a smooth domain Omega subset of R-N such that 0 is an element of partial derivative Omega and given a nonnegative smooth function zeta on partial derivative Omega, we study the behavior near 0 of positive solutions of -Delta u = u(q) in Omega such that u = zeta on partial derivative Omega{0}. We prove that if N+1/N-1 < q < N-2/N-2, then u(x) <= C broken vertical bar x broken vertical bar(-2/q-1) and we compute the limit of broken vertical bar x broken vertical bar(-2/q-1)u(x) as x -> 0. We also investigate the case q = N+1/N-1 . The proofs rely on the existence and uniqueness of solutions of related equations on spherical domains.

Document type Article de périodique (Journal article)
Access type Accès libre
Publication date 2011
Language Anglais
Journal information "Calculus of Variations and Partial Differential Equations" - Vol. 40, no. 1-2, p. 183-221 (2011)
Peer reviewed yes
Publisher Springer ((Germany) Heidelberg)
issn 0944-2669
e-issn 1432-0835
Publication status Publié
Affiliations UCL - SST/IRMP - Institut de recherche en mathématique et physique
Université François Rabelais - Laboratoire de Mathématiques et Physique Théorique
Links
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Bibliographic reference Ponce, Augusto ; Véron, Laurent ; Bidaut-Véron, Marie-Françoise. Isolated boundary singularities of semilinear elliptic equations. In: Calculus of Variations and Partial Differential Equations, Vol. 40, no. 1-2, p. 183-221 (2011)
Permanent URL http://hdl.handle.net/2078.1/105497