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2021 A Gradient Estimate Related Fractional Maximal Operators for a $p$-Laplace Problem in Morrey Spaces
Thanh-Nhan Nguyen, Minh-Phuong Tran, Cao-Kha Doan, Van-Nghia Vo
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Taiwanese J. Math. Advance Publication 1-21 (2021). DOI: 10.11650/tjm/210202

Abstract

In the present paper, we deal with the global regularity estimates for the $p$-Laplace equations with data in divergence form \[ \operatorname{div}(|\nabla u|^{p-2} \nabla u) = \operatorname{div}(|F|^{p-2} F) \quad \textrm{in $\Omega$}, \] in Morrey spaces with natural data $F \in L^p(\Omega;\mathbb{R}^n)$ and nonhomogeneous boundary data belongs to $W^{1,p}(\Omega)$. Motivated by the work of [M.-P. Tran, T.-N. Nguyen, New gradient estimates for solutions to quasilinear divergence form elliptic equations with general Dirichlet boundary data, J. Differential Equations 268 (2020), no. 4, 1427-1462], this paper extends that of global Lorentz--Morrey gradient estimates in which the ‘good-$\lambda$’ technique was undertaken for a class of more general equations, and further, global regularity of weak solutions will be given in terms of fractional maximal operators.

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Thanh-Nhan Nguyen. Minh-Phuong Tran. Cao-Kha Doan. Van-Nghia Vo. "A Gradient Estimate Related Fractional Maximal Operators for a $p$-Laplace Problem in Morrey Spaces." Taiwanese J. Math. Advance Publication 1 - 21, 2021. https://doi.org/10.11650/tjm/210202

Information

Published: 2021
First available in Project Euclid: 8 March 2021

Digital Object Identifier: 10.11650/tjm/210202

Subjects:
Primary: 35J62, 35J92, 46E30

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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