一类泛函极小解梯度的处处正则性

EVERYWHERE REGULARITY TO THE GRADIENT OF SOLUTIONS OF MINIMIZERS OF A CLASS OF FUNCTIONALS

本文考虑向量值函数的泛函J(u)=intergral from G f(|▽u|~2)dx u∈W_p^1(G,E_N),p≥2,N>1的极小问题,证明解梯度在 G 内的处处正则性.这是 Giaquinta-Modica 相应结果的改进.

It is considered the minimum problem of the functionalJ(u)=integral from G f(|▽u|~2)dxfor the vector valued function u∈W_p^1(G,E^N),p≥2,N>1.The everywhereregularity in G for the gradient of solutions is proved.This is an improv-ment of the corresponding result given by Giaquinta-Modica.