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 E-mail:zwl267@163.com;320029374@qq.com;59653147@qq.com
  • Supported by:
    the NSFC(11801259);the NSFC(11461048);the NSF of Jiangxi Province(20202BABL201009);the Education Department of Jiangxi Province(GJJ170604)

Abstract:

In this paper, we consider a class of nonlinear degenerate elliptic equations of the form div(a(x,u,u))+b(x)g(u)+B(x,u,u)=f(x), where the principal part degenerates on {u=0}. Even if f only belongs to L1(Ω), 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
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