Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1405-1414.

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

Weilin Zou*(),Yuanchun Ren(),Meipin Xiao()   

  1. College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063
  • Received:2020-07-16 Online:2021-10-26 Published:2021-10-08
  • Contact: Weilin Zou;;
  • Supported by:
    the NSFC(11801259);the NSFC(11461048);the NSF of Jiangxi Province(20202BABL201009);the Education Department of Jiangxi Province(GJJ170604)


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