TY - JOUR
T1 - The Regularity for Solutions of Variational Inequalities
AU - Liang , Xiting
JO - Journal of Partial Differential Equations
VL - 2
SP - 145
EP - 158
PY - 1995
DA - 1995/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5648.html
KW - Elliptic variational inequality
KW - one-sided obstacle problem
KW - boundedness
KW - Holder continuity
KW - C^{1
KW - α} regularity
AB -  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.