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Polyharmonic capacity and Wiener test of higher order
Univ Minnesota, MN 55455 USA.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2018 (English)In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 211, no 2, p. 779-853Article in journal (Refereed) Published
Abstract [en]

In the present paper we establish the Wiener test for boundary regularity of the solutions to the polyharmonic operator. We introduce a new notion of polyharmonic capacity and demonstrate necessary and sufficient conditions on the capacity of the domain responsible for the regularity of a polyharmonic function near a boundary point. In the case of the Laplacian the test for regularity of a boundary point is the celebrated Wiener criterion of 1924. It was extended to the biharmonic case in dimension three by Mayboroda and Mazya (Invent Math 175(2):287-334, 2009). As a preliminary stage of this work, in Mayboroda and Mazya (Invent Math 196(1):168, 2014) we demonstrated boundedness of the appropriate derivatives of solutions to the polyharmonic problem in arbitrary domains, accompanied by sharp estimates on the Green function. The present work pioneers a new version of capacity and establishes the Wiener test in the full generality of the polyharmonic equation of arbitrary order.

Place, publisher, year, edition, pages
SPRINGER HEIDELBERG , 2018. Vol. 211, no 2, p. 779-853
National Category
Geometry
Identifiers
URN: urn:nbn:se:liu:diva-144873DOI: 10.1007/s00222-017-0756-yISI: 000422955900006OAI: oai:DiVA.org:liu-144873DiVA: diva2:1181733
Note

Funding Agencies|Alfred P. Sloan Fellowship; NSF [DMS 1344235, DMS 1220089]; UMN MRSEC Seed grant [DMR 0212302]; Simons Fellowship in Mathematical Sciences; Ministry of Education and Science of the Russian Federation [02.a03.21.0008]

Available from: 2018-02-09 Created: 2018-02-09 Last updated: 2018-02-09

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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  • Other style
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  • de-DE
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  • sv-SE
  • Other locale
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