Regularity for some nonlinear elliptic problems

doi:10.3969/j.issn.1000-1565.2023.03.001

Journal of Hebei University(Natural Science Edition) ›› 2023, Vol. 43 ›› Issue (3): 225-229.DOI: 10.3969/j.issn.1000-1565.2023.03.001

Regularity for some nonlinear elliptic problems

HUANG Miaomiao^1,2, ZHAO Xueyi¹, FENG Heping³

1.College of Mathematics and Computer Science, Hanjiang Normal University, Shiyan 442000, China; 2.Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, China; 3.Intelligent Engineering Department, Hebei Software Institute, Baoding 071002, China

Received:2022-05-22 Online:2023-05-25 Published:2023-06-15

Abstract

Abstract: When the source function of elliptic partial differential equation is a function of independent variable, unknown function of independent variable and partial derivative of unknown function, the boundary value problem of nonlinear elliptic equation is studied. By using the generalized Stampacchia lemma and the analysis technique of Sobolev space, the regularity of the solution of the boundary value problem of elliptic equation under some coercivity and controlled growth assumptions is obtained.

Key words: regularity, elliptic equation, boundary vale problem, Stampacchia lemma

CLC Number:

O175.23

HUANG Miaomiao, ZHAO Xueyi, FENG Heping. Regularity for some nonlinear elliptic problems[J]. Journal of Hebei University(Natural Science Edition), 2023, 43(3): 225-229.

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Regularity for some nonlinear elliptic problems

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