系数的L1相互关系对非线性退化椭圆方程解的正则性的影响

Abstract

Abstract:

In this paper, we consider a class of nonlinear degenerate elliptic equations of the form $-\mbox{div}(a(x,u,\nabla u))+b(x)g(u)+B(x,u,\nabla u)=f(x)$, where the principal part degenerates on $\{u=0\}$. Even if $f$ only belongs to $L^{1}(\Omega)$, the existence of bounded weak solutions are proven. This generalizes, to some extent, previous results.

Key words: Degenerate elliptic equations, L¹ coefficients, Bounded weak solutions, Regularizing effect

CLC Number:

O175.2

Weilin Zou,Yuanchun Ren,Meipin Xiao. Regularizing Effect of L¹ Interplay Between Coefficients in Nonlinear Degenerate Elliptic Equations[J].Acta mathematica scientia,Series A, 2021, 41(5): 1405-1414.

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Regularizing Effect of L¹ Interplay Between Coefficients in Nonlinear Degenerate Elliptic Equations

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Regularizing Effect of L¹ Interplay Between Coefficients in Nonlinear Degenerate Elliptic Equations