W1,p(·)-Regularity for a Class of Non-uniformly Elliptic Problems with Orlicz Growth

We prove a local W 1 , p ( · ) -regularity for the distributional solutions to double phase elliptic equations with Orlicz growth, and the variable exponents p ( x ) > 1 satisfying the log-Hölder continuity. Moreover, we establish a local Calderón–Zygmund estimate for asymptotically regular doubl...

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Veröffentlicht in:	Mediterranean journal of mathematics 2022, Vol.19 (6)
Hauptverfasser:	Liang, Shuang, Gao, Hongya, Zheng, Shenzhou
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Sprache:	eng
Schlagworte:	Continuity (mathematics) Elliptic functions Mathematics Mathematics and Statistics Regularity
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container_title	Mediterranean journal of mathematics
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description	We prove a local W 1 , p ( · ) -regularity for the distributional solutions to double phase elliptic equations with Orlicz growth, and the variable exponents p ( x ) > 1 satisfying the log-Hölder continuity. Moreover, we establish a local Calderón–Zygmund estimate for asymptotically regular double phase elliptic problems with Orlicz growth, which means that the nonlinearity is getting close to the regular problems when the gradient of its solution goes to infinity.
doi_str_mv	10.1007/s00009-022-02176-2
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title	W1,p(·)-Regularity for a Class of Non-uniformly Elliptic Problems with Orlicz Growth
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