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

Mselati, Benoiti

Couverture souple

ISBN 10 : 0821835092 ISBN 13 : 9780821835098

Editeur : American Mathematical Society, 2004

Synopsis

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2004
• Langue: anglais
• ISBN 10: 0821835092
• ISBN 13: 9780821835098
• Reliure: Broché
• Coordonnées du fabricant: non disponible
• Personne responsable: Mare Nostrum Group B.V.; gpsr@mare-nostrum.co.uk; ; Doelen 72; Breda; 4831 GR; Pays-Bas