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Advances in Calculus of Variations

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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 ⊆ ℝl 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


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. Volume 2, Issue 1, Pages 1–16, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/ACV.2009.001, February 2009

Citing Articles

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[1]
Matthew K. Cooper
Calculus of Variations and Partial Differential Equations, 2015
[2]
Jay Hineman, Tao Huang, and Chang-You Wang
Calculus of Variations and Partial Differential Equations, 2014, Volume 50, Number 3-4, Page 491
[3]
Huajun Gong, Tobias Lamm, and Changyou Wang
Calculus of Variations and Partial Differential Equations, 2012, Volume 45, Number 1-2, Page 165
[4]
Tao Huang and Changyou Wang
Advances in Calculus of Variations, 2011, Volume 4, Number 2

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