Existence and regularity of solution of mixed boundary value problem of a Busemann-equation with nonlinear absorb term

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:357

Article

Xu, Zhonghai¹  Liu, Shengquan¹  Feng, Zhenguo¹ 

[1] NE Dianli Univ, Coll Sci, Jilin 132013, Peoples R China

关键词: Degenerate elliptic equation;    Busemann-equation;    Mixed boundary problem;    Prior estimates;   

DOI  :  10.1016/j.jmaa.2009.04.007

来源: Elsevier

【 摘 要 】

The Busemann-equation is a classical equation coming from fluid dynamics. The well-posed problem and regularity of solution of Busemann-equation with nonlinear term are interesting and important. The Busemann-equation is elliptic in y > 0 and is degenerate at the line y = 0 in R-2. With a special nonlinear absorb term, we study a nonlinear degenerate elliptic equation with mixed boundary conditions in a piecewise smooth domain. By means of elliptic regularization technique, a delicate prior estimate and compact argument, we show that the solution of mixed boundary value problem of Busemann-equation is smooth in the interior and Lipschitz continuous up to the degenerate boundary on some conditions. The result is better than the result of classical boundary degenerate elliptic equation. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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