$\Gamma$-Limiti di ostacoli

De Giorgi, Ennio ; Dal Maso, Gianni ; Longo, Placido

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 68 (1980) no. 6, pp. 481-487

Résumé

In this paper we show that all limits of sequences of minimum problems of the type $$ \min \Big \{ \int |Du|^{2} + \int |u|^{2} : u \ge \psi_{h} \quad \text{ on } B \Big \}$$ are minimum problems of the type $$ \min \Big\{ \int |Du|^{2} + \int |u|^{2} + \int_{B} f(x,u) d\mu + \nu (B) \Big\}$$ where $\mu$, $\nu$ are positive Radon measures, $\mu \in H^{-1}$ and $f(x,u)$ is convex and non-increasing in the variable $u$.