A-调和方程很弱解的正则性

Regularity for Very Weak solutions of A-Harmonic Equations

本文证明了二阶拟线性偏微分方程很弱解的正则性．若ｕ是（１）的一个很弱解并属于一个合适的包含Ｗ１，ｐ ｌｏｃ（ ）的空间，则ｕ属于 （ ），即ｕ是（１）通常意义下的弱解．变分积分弱极值的同样结果被得到．

A regularity property for very weak solutions of quasilinear partial differential equations of second order is proved. If u is a very weak solution to (1) and belongs to a proper space, which contains W(), then u W( ), i.e., u is a weak solution to (1) in the usual sense. Similar result is given to weak minima of variational integrals.