An optimization problem with volume constrain for a degenerate quasilinear operator.

JULIAN FERNANDEZ BONDER; MARTÍNEZ, S. R.; WOLANSKI, NOEMI IRENE

JOURNAL OF DIFFERENTIAL EQUATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2006 vol. 227 p. 80 - 101

0022-0396

We consider the optimization problem of minimizing $int_{Omega} | abla u|^p dx$ with a constrain on the volume of ${u > 0}$. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution $u$ is locally Lipschitz continuous and that the free boundary, $partial {u > 0}$ , is smooth. | abla u|^p dx$ with a constrain on the volume of ${u > 0}$. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution $u$ is locally Lipschitz continuous and that the free boundary, $partial {u > 0}$ , is smooth.