Some Limiting Situations for Semilinear Elliptic Equations
نویسندگان
چکیده
— The objective of this mini-course is to take a look at a standard semilinear partial differential equation −∆u = λf(u) on which we show the use of some basic tools in the study of elliptic equation. We will mention the maximum principle, barrier method, blow-up analysis, regularity and boot-strap argument, stability, localization and quantification of singularities, Pohozaev identities, moving plane method, etc. Résumé (Quelques situations limites pour les équations semi-linéaires elliptiques) L’objectif de ce mini-cours est de jeter un coup d’œil sur une équation aux dérivées partielles standard −∆u = λf(u), avec laquelle nous allons montrer quelques outils de base dans l’étude des équations elliptiques. Nous mentionnerons le principe du maximum, la méthode de barrière, l’analyse de blow-up, la régularité, l’argument de boot-strap, la stabilité, la localisation et quantification de singularités, les identités de Pohozaev, la méthode du plan mobile, etc.
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