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Boundary C 1,α regularity for variational inequalities
Author(s) -
Lin Fang Hua,
Li Yi
Publication year - 1991
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160440605
Subject(s) - fang , mathematics , citation , combinatorics , variational inequality , boundary (topology) , algebra over a field , calculus (dental) , computer science , pure mathematics , library science , mathematical analysis , medicine , ecology , dentistry , biology
In this paper we will consider the regularity problem for the following obstacle problem. (1.1) inf Z jrvj p dx among the functions in W(''), where is a bounded C 2 domain in < n (n 2) and ' and are C 2-functions deened on w i t h ', a n d 1 < p < 1 such t h a t W('') = fv 2 W 1p (() : v ; ' 2 W 1p 0 (() and v a.e. in g Remark 1.1. The C 2 assumptions on and ' are purely technical to avoid complications , as the reader may nd out later. Because of the convexity of the integrand, (1.1) has a unique solution u satisfying the variational inequality (see, for example LQ]).