Calculus of Variations and Geometric Measure Theory

G. Carita - E. Zappale

Relaxation for an optimal design problem with linear growth and perimeter penalization

created on 15 Jul 2014


Accepted Paper

Inserted: 15 jul 2014

Journal: Proc. Royal Soc. Edinburgh A
Year: 2014


The paper is devoted to the relaxation and integral representation in the space of functions of bounded variation for an integral energy arising from optimal design problems. The presence of a perimeter penalization is also considered in order to avoid non existence of admissible solutions, besides this leads to an interaction in the limit energy. Also more general models have been taken into account.

Keywords: Relaxation, functions of bounded variation, perimeter penalization.