Regularity for Very Weak Solutions of A-Harmonic Equation with Weight

- Journal title : Kyungpook mathematical journal
- Volume 49, Issue 2, 2009, pp.195-202
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2009.49.2.195

Title & Authors

Regularity for Very Weak Solutions of A-Harmonic Equation with Weight

Gao, Hong-Ya; Zhang, Yu; Chu, Yu-Ming;

Gao, Hong-Ya; Zhang, Yu; Chu, Yu-Ming;

Abstract

This paper deals with very weak solutions of the A-harmonic equation = 0 (*) with the operator satisfies some coercivity and controllable growth conditions with Muckenhoupt weight. By using the Hodge decomposition with weight, a regularity property is proved: There exists an integrable exponent < p, such that every very weak solution with < r < p belongs to . That is, u is a weak solution to (*) in the usual sense.

Keywords

A-harmonic equation;Muckenhoupt weight;regularity; Hodge decomposition;

Language

English

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