具有多项式增长的退缩拟线性抛物变分不等式

Degenerate Variational Inequalities of Quasilinear Parabolic Type with Polynomial Growth

考虑拟线性抛物型变分不等式：ｕ∈Ｋａ．ｅ．，〈Ａｕ′，ｖ－ｕ〉∫Ωａｉ（ｘ，ｕ，ｕ）（ｖ－ｕ）ｘｉｄｘ＋∫Ωａ（ｘ，ｕ，ｕ）（ｖ－ｕ）ｄｘ≥０ａ．ｅ．ｔ，ｖ∈Ｋ，这里Ｋ为闭凸集，Ａ为非１—１，可能退缩的线性算子．在ａｉ（ｘ，ｕ，ｐ），ａ（ｘ，ｕ，ｐ）关于ｐ，ｕ具有多项式增长的假设下，得到了正则解的存在性和唯一性．特别是，当Ａ＝Ｉ时，我们便得到文［１０］的结果．

We consider quasilinear parabolic variational inequalities of the formu∈K a.e.,〈Au′,v-u〉+∫Ωai(x,u,u)(v-u)xidx+∫Ωa(x,u,u)(v-u)dx≥0a.e. t,v∈K,where A is not 1-1 and may vanish, K be closed and convex set. We obtain the existence, uniqueness and regularity under the assumption of ai(x,u,p) and a(x,u,p) with polynomial growth for u and p by means of the approximation and penalization method.