NEUMANN LAPLACIAN ON A DOMAIN WITHTANGENTIAL COMPONENTS IN THE BOUNDARY

Serguei A. Nazarov; Jan Sokolowski; Jari Taskinen

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NEUMANN LAPLACIAN ON A DOMAIN WITHTANGENTIAL COMPONENTS IN THE BOUNDARY

机译：诺依曼·拉普拉斯（NEUMANN LAPLACSIAN）在边界中具有切向分量的域上

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We study the Neumann problem for the Poisson equation in a domain where twoboundary components are tangential at a single point, such that a geometrical irregularity of therotational cusp type is formed. We derive necessary and sufficient conditions for the existence of asolution with a finite Dirichlet integral.

机译：我们研究了泊松方程的诺依曼问题，在该域中，两个边界分量在单个点上相切，从而形成了旋转尖点类型的几何不规则性。我们推导出具有有限狄利克雷积分的解存在的必要和充分条件。

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《Annales Academiae Scientiarum Fennicae. Mathematica》 |2009年第1期|131-143|共13页
作者
Serguei A. Nazarov; Jan Sokolowski; Jari Taskinen;
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作者单位

University of Helsinki, Department of Mathematics and Statistics P.O. Box 68, 00014 Helsinki, Finland;

Russian Academy of Sciences, Institute of Problems of Mechanical EngineeringV.O., Bolshoi pr., 61, 199178, St. Petersburg, Russia;

Universite Henri Poincare Nancy 1, Departement de Mathematiques B.P. n. 239, 54506 Vandoeuvrc les Nancy Cedex, France;

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正文语种英语
中图分类数学;
关键词
Poisson equation; Neumann problem; nonsmooth boundary; rotational cusp;

机译：泊松方程;诺依曼问题;非平滑边界;旋转尖点;

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NEUMANN LAPLACIAN ON A DOMAIN WITHTANGENTIAL COMPONENTS IN THE BOUNDARY

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