Nonlinear obstacle problems with double phase in the borderline case

Sun Sig Byun; Yumi Cho; Jehan Oh

doi:10.1002/mana.201800277

Nonlinear obstacle problems with double phase in the borderline case

Sun Sig Byun
, Yumi Cho
, Jehan Oh

Seoul National University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 (Formula presented.) -growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.

Original language	English
Pages (from-to)	651-669
Number of pages	19
Journal	Mathematische Nachrichten
Volume	293
Issue number	4
DOIs	https://doi.org/10.1002/mana.201800277
State	Published - 1 Apr 2020

Keywords

35B65
35J87
BMO coefficient
Calderón–Zygmund estimate
double phase problem
obstacle problem
Reifenberg flat domain

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10.1002/mana.201800277

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title = "Nonlinear obstacle problems with double phase in the borderline case",

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 (Formula presented.) -growth. We obtain an optimal global Calder{\'o}n–Zygmund type estimate for the obstacle problem with double phase in the borderline case.",

keywords = "35B65, 35J87, BMO coefficient, Calder{\'o}n–Zygmund estimate, double phase problem, obstacle problem, Reifenberg flat domain",

author = "Byun, \{Sun Sig\} and Yumi Cho and Jehan Oh",

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AU - Cho, Yumi

AU - Oh, Jehan

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N2 - 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 (Formula presented.) -growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.

AB - 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 (Formula presented.) -growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.

KW - 35B65

KW - 35J87

KW - BMO coefficient

KW - Calderón–Zygmund estimate

KW - double phase problem

KW - obstacle problem

KW - Reifenberg flat domain

UR - https://www.scopus.com/pages/publications/85078669447

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DO - 10.1002/mana.201800277

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SP - 651

EP - 669

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 4

ER -

Nonlinear obstacle problems with double phase in the borderline case

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Keywords

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