An optimization problem with volume constraint for an inhomogeneous operator with nonstandard growth

Claudia Lederman; Noemi Wolanski

doi:10.3934/dcds.2020391

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2021, Volume 41, Issue 6: 2907-2946. Doi: 10.3934/dcds.2020391

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An optimization problem with volume constraint for an inhomogeneous operator with nonstandard growth

Claudia Lederman^, and
Noemi Wolanski

IMAS - CONICET and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina

^* Corresponding author: clederma@dm.uba.ar
^* Corresponding author: clederma@dm.uba.ar

Received: October 2020

Early access: December 2020

Published: June 2021

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Abstract

We consider an optimization problem with volume constraint for an energy functional associated to an inhomogeneous operator with nonstandard growth. By studying an auxiliary penalized problem, we prove existence and regularity of solution to the original problem: every optimal configuration is a solution to a one phase free boundary problem—for an operator with nonstandard growth and non-zero right hand side—and the free boundary is a smooth surface.

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Mathematics Subject Classification: Primary: 35R35, 35J20; Secondary: 35J70, 35J60, 49Q10, 49K20, 35B65.

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