Besov Regularity of Weak solutions to a Class of Nonlinear Elliptic Equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929249061961728 |
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| author | Cheng, Huimin Zhou, Feng |
| author_facet | Cheng, Huimin Zhou, Feng |
| contents | In this article, we study a Besov regularity estimate of weak solutions to a class of nonlinear elliptic equations in divergence form. The main purpose is to establish Calderon-Zygmund type estimate in Besov spaces with more general assumptions on coefficients, non-homogeneous term and integrable index. By involving the Sharp maximal function, we establish an oscillation estimate of weak solutions in Orlicz-Sobolev spaces. By deriving a higher integrability estimate of weak solutions, we obtain the desired regularity estimate which expands the Calderon-Zygmund theory for nonlinear elliptic equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_12975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Besov Regularity of Weak solutions to a Class of Nonlinear Elliptic Equations Cheng, Huimin Zhou, Feng Analysis of PDEs In this article, we study a Besov regularity estimate of weak solutions to a class of nonlinear elliptic equations in divergence form. The main purpose is to establish Calderon-Zygmund type estimate in Besov spaces with more general assumptions on coefficients, non-homogeneous term and integrable index. By involving the Sharp maximal function, we establish an oscillation estimate of weak solutions in Orlicz-Sobolev spaces. By deriving a higher integrability estimate of weak solutions, we obtain the desired regularity estimate which expands the Calderon-Zygmund theory for nonlinear elliptic equations. |
| title | Besov Regularity of Weak solutions to a Class of Nonlinear Elliptic Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.12975 |