Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation - Brossura

Mselati, Benoiti

Brossura

ISBN 10: 0821835092 ISBN 13: 9780821835098

Casa editrice: Amer Mathematical Society, 2004

Riassunto

We are concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$. We prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], thus answering a major open question of [Dy02]. In this title, a probabilistic formula for a solution in terms of its fine trace and of the Brownian snake is also provided. A major role is played by the solutions which are dominated by a harmonic function in $D$. The latters are called moderate in Dynkin's terminology. We show that every nonnegative solution of $\Delta u = u^2$ in $D$ is the increasing limit of moderate solutions.

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Product Description

Book by Benoit Mselati

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 0821835092
• ISBN 13: 9780821835098
• Rilegatura: Copertina flessibile
• Contatto del produttore: non disponibile
• Persona responsabile: Mare Nostrum Group B.V.; gpsr@mare-nostrum.co.uk; ; Doelen 72; Breda; 4831 GR; Paesi Bassi