Vol. 13, No. 5, 2020

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Regularity results for generalized double phase functionals

Sun-Sig Byun and Jehan Oh

Vol. 13 (2020), No. 5, 1269–1300
Abstract

We consider a wide class of functionals with the property of changing their growth and ellipticity properties according to the modulating coefficients in the framework of Musielak–Orlicz spaces. In particular, we provide an optimal condition on the modulating coefficient to establish the Hölder regularity and Harnack inequality for quasiminimizers of the generalized double phase functional with (G,H)-growth for two Young functions G and H.

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Keywords
double phase functional, Lavrentiev phenomenon, nonstandard growth, quasiminimizer, regularity
Mathematical Subject Classification 2010
Primary: 49N60
Secondary: 35B65, 35J20
Milestones
Received: 15 August 2017
Revised: 30 April 2019
Accepted: 11 June 2019
Published: 27 July 2020
Authors
Sun-Sig Byun
Department of Mathematical Sciences and Research Institute of Mathematics
Seoul National University
Seoul
South Korea
Jehan Oh
Department of Mathematics
Kyungpook National University
Daegu
South Korea