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Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation
Brown University.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2009 (English)In: INVENTIONES MATHEMATICAE, ISSN 0020-9910 , Vol. 175, no 2, 287-334 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2009. Vol. 175, no 2, 287-334 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-16514DOI: 10.1007/s00222-008-0150-xOAI: oai:DiVA.org:liu-16514DiVA: diva2:158120
Available from: 2009-01-30 Created: 2009-01-30 Last updated: 2009-01-30

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G. Maz'ya , Vladimir

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