A constrained shape optimization problem in Orlicz-Sobolev spaces

JOAO VITOR DA SILVA; ARIEL SALORT; ANALÍA SILVA; JUAN F. SPEDALETTI

JOURNAL OF DIFFERENTIAL EQUATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2019

0022-0396

In this manuscript we study the following optimization problem: given a bounded and regular domain Omega ⊂ R^N we look for an optimal shape for the "W−vanishing window" on the boundary with prescribed measure over all admissible profiles in the framework of the Orlicz-Sobolev spaces associated to constant for the "Sobolev trace embedding". In this direction, we establish existence of minimizer profiles and optimal sets, as well as we obtain further properties for such extremals. Finally, we also place special emphasis on analyzing the corresponding optimization problem involving an "A−vanishing hole" (inside the domain) with volume constraint.