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April 2022 Gradient estimates in anisotropic Lorentz spaces to general elliptic equations of p-growth
Hong Tian, Shenzhou Zheng
Rocky Mountain J. Math. 52(2): 727-748 (April 2022). DOI: 10.1216/rmj.2022.52.727

Abstract

We prove a global mixed-norm gradient estimate in the framework of anisotropic Lorentz spaces to general elliptic equations of p-growth under weak regularity data. It is assumed that the principle coefficients are small BMO seminorm in x-variable, and the boundary of underlying domain is locally C0,1-smooth with a small Lipschitz constant.

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Hong Tian. Shenzhou Zheng. "Gradient estimates in anisotropic Lorentz spaces to general elliptic equations of p-growth." Rocky Mountain J. Math. 52 (2) 727 - 748, April 2022. https://doi.org/10.1216/rmj.2022.52.727

Information

Received: 27 February 2021; Revised: 15 July 2021; Accepted: 15 July 2021; Published: April 2022
First available in Project Euclid: 17 May 2022

Digital Object Identifier: 10.1216/rmj.2022.52.727

Subjects:
Primary: 35D30 , 35J92
Secondary: 46E30

Keywords: anisotropic Lorentz spaces , BMO discontinuous coefficients , C0,1-domain with small Lipschitz constant , Calderón–Zygmund estimates , general elliptic equation of p-growth

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 2 • April 2022
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