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Zaremba problem with degenerate weights

  • Anna Kh. Balci ORCID logo and Ho-Sik Lee ORCID logo EMAIL logo
Published/Copyright: November 17, 2024

Abstract

We present new regularity result in the study of elliptic equations with mixed boundary conditions. We obtain small higher integrability of the gradient (Meyers property). The result is new for both linear and nonlinear equations with degenerate coefficients with a new sharp Maz’ya-type capacity condition on the part with Dirichlet boundary condition, while prior research was limited to uniformly elliptic weights.

MSC 2020: 35J60; 35B65; 35J15

Communicated by Juha Kinnunen


Award Identifier / Grant number: SFB 1283/2 2021 – 317210226

Award Identifier / Grant number: GRK 2235/2 2021 – 282638148

Funding statement: Anna Kh. Balci is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – SFB 1283/2 2021 – 317210226, Charles University in Prague PRIMUS/24/SCI/020 and Research Centre program No. UNCE/24/SCI/005. Ho-Sik Lee is funded by Deutsche Forschungsgemeinschaft through GRK 2235/2 2021 – 282638148.

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Received: 2024-04-22
Accepted: 2024-07-29
Published Online: 2024-11-17
Published in Print: 2025-07-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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