Calculus of Variations and Geometric Measure Theory

M. Carriero - A. Leaci

$S^k$-valued maps minimizing the $L^p$ norm of the gradient with free discontinuities

created by leaci on 15 Apr 2023


Published Paper

Inserted: 15 apr 2023

Journal: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume: s. IV, v. 18
Number: 3
Pages: 321-352
Year: 1991
Links: Published paper


In this paper, we study two new variational problems involving $S^k$-valued maps, where $S^k = \{ z \in {\mathbb R}^{k+1}, \Vert z \Vert = 1 \} $. We deal with free discontinuity problems since a solution is a pair $(K, u)$, where $K$ is a (a-priori unknown) closed set and $u$ is a map suitably smooth outside of K. These problems can be regarded as a possible schematization of problems in mathematical physics in which both volume forces and surface tensions are present.

Keywords: calculus of variations, free discontinuity problems