Gradient estimates for non-uniformly elliptic problems with BMO nonlinearity

We provide a new approach to obtain Calderón-Zygmund type estimates for non-uniformly elliptic equations with discontinuous nonlinearities of double phase growth. This approach, which is based on a small higher integrability result for the gradient of weak solutions to the associated homogeneous pro...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 520; no. 1; p. 126894
Main Authors Byun, Sun-Sig, Lee, Ho-Sik
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.2023
Subjects
BMO space
Calderón-Zygmund estimate
Double phase problem
Extrapolation
Double phase problem
Extrapolation
Calderón-Zygmund estimate
BMO space
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Summary:We provide a new approach to obtain Calderón-Zygmund type estimates for non-uniformly elliptic equations with discontinuous nonlinearities of double phase growth. This approach, which is based on a small higher integrability result for the gradient of weak solutions to the associated homogeneous problems together with extrapolation from Muckenhoupt weights, enables us to find a proper comparison estimate of approximation by imposing merely a small BMO assumption on the nonlinearity with respect to the x-variable. As a consequence, we are able to prove an optimal regularity theory for a larger class of double phase problems with discontinuous nonlinearities in the literature.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2022.126894