泛函极小与椭圆型微分方程解的可积性

发布时间：2018-01-13 13:05

本文关键词：泛函极小与椭圆型微分方程解的可积性　出处：《河北大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文研究积分泛函极小点的局部正则性其中f(x,z,s)满足这里f0(x,s,z)满足某增长条件,且f1(x,s,z)满足某控制条件.另外,本文还研究非齐次椭圆方程解的局部正则性和局部有界性此外,在积分泛函中当f(x,z)满足某些单调性条件时在向量域上研究了泛函极小的极小值原理,以及与之对应的椭圆方程组弱解的极大值和极小值原理.最后,对A-调和方程很弱解的高阶可积性进行了研究.
[Abstract]:In this paper, we study the local regularity of the minimum point of the integral functional, where f ~ (x) ~ (()) satisfies a certain growth condition, and f _ (1) ~ (x ~ (()) ~ () ~ () satisfies a certain control condition. In this paper, we also study the local regularity and local boundedness of solutions of inhomogeneous elliptic equations. In addition, we study the minima principle of functional minimization in vector domain when fnxnz) satisfies some monotonicity conditions in integral Functionals. And the maximum and minimum principle of the weak solutions of the corresponding elliptic equations. Finally, the high order integrability of the very weak solutions of the A- harmonic equations is studied.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.25

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