一类A -调和方程的障碍问题的很弱解的全局正则性

Abstract

Abstract:

Using Hodge decomposition theorem, the local and the global W^1, ^q(Ω)-regularity results for very weak solutions to the obstacle problems associated with the following non-homogeneous A-harmonic equations

-div(A(x, Du(x)))=f(x, u(x))
are obtained under certain conditions on A(x, Du(x)), f(x, u(x)) listed in the context. The results generalize the corresponding results in related literatures. The results can be widely applied to optimal control problems.

Key words: Non-homogeneous A-harmonic equations, Obstacle problems, Optimal control, Hodge decomposition, Global W^1, ^q(Ω)-regularity

CLC Number:

35J60

ZHOU Shu-Qing, HU Zhen-Hua, PENG Dong-Yun. Global Regularity for Very Weak Solutions to Obstacle Promlems Corresponding to a Class of A-Harmonic Equations[J].Acta mathematica scientia,Series A, 2014, 34(1): 27-38.

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Global Regularity for Very Weak Solutions to Obstacle Promlems Corresponding to a Class of A-Harmonic Equations

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