奇异对流方程组非常弱解的梯度正则性

Abstract

Abstract:

This paper deals with the partial regularity of very weak solutions to elliptic equations with singular convective. By the properties of Lorentz space and its relation to Lebesgue space, we conclude that the elliptic systems with singular convection have very weak solutions in $L^p$ space. Then, it can be found from Hodge decomposition that the very weak solutions of Dirichlet problem are actually the classical weak solutions. Finally, combining with A-harmonic approximation technique, we further find that the obtained weak solution has partial regularity; especially, the regularity is optimal.

Key words: Very weak solution, Hodge composition, Singular convection, A-harmonic approximation technique

CLC Number:

O175.2

Chen Shuhong,Tan Zhong. Gradient Regularity of Very Weak Solution to Elliptic Equations with Singular Convection[J].Acta mathematica scientia,Series A, 2023, 43(3): 713-732.

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Gradient Regularity of Very Weak Solution to Elliptic Equations with Singular Convection

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