A constrained shape optimization problem in Orlicz-Sobolev spaces

DA SILVA, JOÃO VITOR; SALORT, ARIEL M.; SILVA, ANALÍA; SPEDALETTI, JUAN F.

JOURNAL OF DIFFERENTIAL EQUATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2019 vol. 267 p. 5493 - 5520

0022-0396

In this manuscript we study the following optimization problem: given a bounded and regular domain Ω⊂RN 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.