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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board Member: Armstrong, Scott N. / Astala, Kari / Colding, Tobias / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Finster, Felix / Gianazza, Ugo / Gursky, Matthew / Hardt, Robert / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / McCann, Robert / Mingione, Giuseppe / Nystrom, Kaj / Pacard, Frank / Preiss, David / Riviére, Tristan / Schaetzle, Reiner / Silvestre, Luis

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Online
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1864-8266
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Boundary regularity for polyharmonic maps in the critical dimension

Tobias Lamm
  • Max-Planck-Institute for Gravitational Physics, Am Mühlenberg 1, 14476 Golm, Germany. E-mail:
/ Changyou Wang
  • Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA. E-mail:
Published Online: 2009-02-03 | DOI: https://doi.org/10.1515/ACV.2009.001

Abstract

We consider the Dirichlet problem for intrinsic and extrinsic k-polyharmonic maps from a bounded, smooth domain Ω ⊆ ℝ2k to a compact, smooth Riemannian manifold N ⊆ ℝ l without boundary. For any smooth boundary data, we show that any k-polyharmonic map uW k,2(Ω, N) is smooth near the boundary ∂Ω.

Keywords.: Polyharmonic maps; boundary regularity

About the article

Received: 2008-03-13

Revised: 2008-06-26

Published Online: 2009-02-03

Published in Print: 2009-02-01


Citation Information: Advances in Calculus of Variations, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/ACV.2009.001.

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