拟线性椭圆型变分不等式解的正则性

ON REGULARITIES OF WEAK SOLUTIONS OF QUASILINEAR ELLIPTIC VARIATIONAL INEQUALITIES

本文沿用H.Brezis在《单边问题》中提出的方法,引进“加权强迫性条件”和“相对一致李普希兹条件”,证明了一类具有任意增长阶的拟线性椭圆型变分不等式的属于W^(1,m)(Ω,R^N)(m≥2)类广义解的W^(2,m)(Ω,R)类正则性,推广了M.Cocu和A.Radoslovescu的结果。

In this paper,by using the method proposed by H.Brezis and introducing“Weighted Coercive”and“Related uniformally Lipschitz”conditions,we haveextended the results of Brezis'and proved that the weak solutions belonging toW^(1,m)(Ω,R^N)to a class of quasilinear elliptic variational inequality with anygrowth order belong to the space W^(2,m)(Ω,R^N),where m≥2.