Nonlinear obstacle problems with double phase in the borderline case

Sun‐Sig Byun, Yumi Cho and Jehan Oh

Mathematische Nachrichten, 2020, vol. 293, issue 4, 651-669

Abstract: In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with (p,q)‐growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.

Date: 2020
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https://doi.org/10.1002/mana.201800277

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