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Date Published: 30/03/2021
Online Published: 31/03/2021
Abstract Views: 179
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DOI: https://doi.org/10.54607/hcmue.js.18.3.2766(2021)
Issue
Vol. 18 No. 3 (2021)
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Articles
How to Cite
Lê , H. P. (2021). A LORENTZ GRADIENT ESTIMATE FOR A CLASS OF MEASURE DATA P-LAPLACE EQUATION WITH P CLOSED TO 1. HCMUE Journal of Science, 18(3), 521. https://doi.org/10.54607/hcmue.js.18.3.2766(2021)

A LORENTZ GRADIENT ESTIMATE FOR A CLASS OF MEASURE DATA P-LAPLACE EQUATION WITH P CLOSED TO 1

Hồng Phúc Lê

Main Article Content

Abstract

 

p-Laplace equation is one of the partial differential equations which has been studied extensively. This equation has many applications in Physics and other sciences. The aim of the present paper is to establish a Lorentz gradient estimate for renormalized solutions to the p-Laplace equation with the data satisfying a Reifenberg domain in the case of p closed to 1. In order to prove the main result, we use a good-λ technique which has been considered in many recent studies. In particular, we used the results of the reverse Hölder’s inequality and the comparison estimate between the solutions of the original problem and the corresponding homogeneous problem in the study by Tran and Nguyen, 2019c to prove the good-λ inequality. In particular, we consider the hypothesis of the Reifenberg domain to obtain a better evaluation in the study by Tran and Nguyen, 2019c.

 

Keywords

Lorentz spaces, measure data, p-Laplace equations, Reifenberg domain

Article Details

References

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