Gradient Estimates of ω-Minimizers to Double Phase Variational Problems with Variable Exponents

Gradient Estimates of ω-Minimizers to Double Phase Variational Problems with Variable Exponents

Abstract We are concerned with an optimal regularity for ω-minimizers to double phase variational problems with variable exponents where the associated energy density is allowed to be discontinuous. We identify basic structure assumptions on the density for the absence of Lavrentiev phenomenon and h...

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Bibliographic Details
Published in:Quarterly journal of mathematics Vol. 72; no. 4; pp. 1191 - 1221
Main Authors: Byun, Sun-Sig, Lee, Ho-Sik
Format: Journal Article
Language:English
Published: UK Oxford University Press 09-12-2021
Online Access:Get full text
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Summary:Abstract We are concerned with an optimal regularity for ω-minimizers to double phase variational problems with variable exponents where the associated energy density is allowed to be discontinuous. We identify basic structure assumptions on the density for the absence of Lavrentiev phenomenon and higher integrability. Moreover, we establish a local Calderón–Zygmund theory for such generalized minimizers under minimal regularity requirements regarding such double phase functionals to the frame of Lebesgue spaces with variable exponents.
ISSN:0033-5606
1464-3847
DOI:10.1093/qmath/haaa067