积分泛函极小值点的弱单调性

Weak monotonicity for minima of variational integrals

弱单调性概念是1994年由J.J.Manfredi引入的,它是研究椭圆型方程正则性理论的有力工具。由于椭圆型方程和变分问题的密切关系,研究变分问题中的弱单调性。利用p-型变分核和Sobolev空间的分析方法,给出了积分泛函极小值点的弱单调性。

The concept of weak monotonicity was introduced by J.J.Manfredi in 1994,and it is an important tool in the study of regularity theory of elliptic PDEs.Duo to the close relationship between elliptic PDEs and variational integrals,weak monotonicity in variational integrals is studied.Weak monotonicity for minima of variational integrals is given by using the variational kernal of type p and the analytical methods in Sobolev spaces.