This paper is an extended version of the lecture delivered at the Summer School on Differential Equations and Calculus of Variations (Pisa, September 16-28, 1996). That lecture was conceived as an introduction to the theory of Gamma-convergence and in particular to the Modica-Mortola theorem; I have tried to replicate the style and the structure of the lecture also in the written version. Thus first come few words on the definition and the meaning of Gamma-convergence, and then we pass to the theorem of L. Modica and S. Mortola. The original idea was to describe both the mechanical motivations which underlay this result and the main ideas of its proof. In particular I have tried to describe a guideline for the proof which would adapt also to other theorems on the same line.
Variational models for phase transitions, an approach via Gamma-convergence
ALBERTI, GIOVANNI
2000-01-01
Abstract
This paper is an extended version of the lecture delivered at the Summer School on Differential Equations and Calculus of Variations (Pisa, September 16-28, 1996). That lecture was conceived as an introduction to the theory of Gamma-convergence and in particular to the Modica-Mortola theorem; I have tried to replicate the style and the structure of the lecture also in the written version. Thus first come few words on the definition and the meaning of Gamma-convergence, and then we pass to the theorem of L. Modica and S. Mortola. The original idea was to describe both the mechanical motivations which underlay this result and the main ideas of its proof. In particular I have tried to describe a guideline for the proof which would adapt also to other theorems on the same line.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
