Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation |
| |
Authors: | Svitlana Mayboroda Vladimir Maz’ya |
| |
Institution: | 1.Department of Mathematics,Brown University,Providence,USA;2.Department of Mathematics,The Ohio State University,Columbus,USA;3.Department of Mathematical Sciences, M&O Building,University of Liverpool,Liverpool,UK;4.Department of Mathematics,Link?ping University,Link?ping,Sweden |
| |
Abstract: | The behavior of solutions to the biharmonic equation is well-understood in smooth domains. In the past two decades substantial
progress has also been made for the polyhedral domains and domains with Lipschitz boundaries. However, very little is known
about higher order elliptic equations in the general setting.
In this paper we introduce new integral identities that allow to investigate the solutions to the biharmonic equation in an
arbitrary domain. We establish:
(1) boundedness of the gradient of a solution in any three-dimensional domain;
(2) pointwise estimates on the derivatives of the biharmonic Green function;
(3) Wiener-type necessary and sufficient conditions for continuity of the gradient of a solution.
Mathematics Subject Classification (2000) 35J40, 35J30, 35B65 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|