关于一类半线性高阶障碍问题解的存在性与正则性

本文考虑一类带互补边界条件的四阶半线性椭圆型变分不等式,应用临界点理论,证明了当半线性项具有超线性增长时解的存在性,并利用L~p估计得到了解的正则性.

The Existence and Regularity of Solutions of a Semilinear Obstacle Problem of Higher Order

In this paper is considered a semilinear elliptic variational inequality of fourth order with complementary boundary conditions. When the semilinear item is superlinearly increasing, the existence of the solutions is proved by applying critical point theory. The regularity is also obtaind with the aid of L~p-estimation.