Existence and regularity of solution of mixed boundary value problem of a Busemann-equation with nonlinear absorb term |
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Authors: | Zhonghai Xu Shengquan Liu Zhenguo Feng |
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Institution: | Science College of Northeast Dianli University, Jilin City 132013, China |
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Abstract: | 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 R2. 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. |
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Keywords: | Degenerate elliptic equation Busemann-equation Mixed boundary problem Prior estimates |
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