The Regularity for Solutions of Variational Inequalities

Abstract

The regularity for solutions of elliptic equations is rather perfectly solved. But it does not so perfect for that of elliptic variational inequalities. In literature only different special situations are considered. Now the boundedness, C^{0,λ} continuity and C^{1,α} regularity are proved for solutions of one-sided obstacle problems under more general structural conditions, in which the growth orders of u are permitted to reach the critical exponents and the growth order ϒ of the gradient in D is permitted to be super critical as 1 < p < n.