HIGHER INTEGRABILITY FOR VERY WEAK SOLUTIONS TO A-HARMONIC EQUATION
GAO HONGYA *
College of Mathematics and Information Science, Hebei University, Baoding, 071002, China.
GUO KAILI
College of Mathematics and Information Science, Hebei University, Baoding, 071002, China.
*Author to whom correspondence should be addressed.
Abstract
This paper deals with higher integrability property for very weak solutions to theA-harmonicequation
div A(x,∇u) = 0,
where the Carath ́eodory function A: Ω×Rn→Rn satisfies some coercivity and growth conditionswhose prototype is
A(x, ξ) = (μ2+|ξ|2)p-2/2 ξ, 1< p≤n.
Keywords: Higher integrability, very weak solution, A-harmonic equation