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Abstract
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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
-growth for two
Young functions
and
.
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Keywords
double phase functional, Lavrentiev phenomenon, nonstandard
growth, quasiminimizer, regularity
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Mathematical Subject Classification 2010
Primary: 49N60
Secondary: 35B65, 35J20
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Milestones
Received: 15 August 2017
Revised: 30 April 2019
Accepted: 11 June 2019
Published: 27 July 2020
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