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Nonlinear obstacle problems with double phase in the borderline case

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  • Sun‐Sig Byun
  • Yumi Cho
  • Jehan Oh

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.

Suggested Citation

  • Sun‐Sig Byun & Yumi Cho & Jehan Oh, 2020. "Nonlinear obstacle problems with double phase in the borderline case," Mathematische Nachrichten, Wiley Blackwell, vol. 293(4), pages 651-669, April.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:4:p:651-669
    DOI: 10.1002/mana.201800277
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