Variationally harmonic maps with general boundary conditions: Boundary regularity

Let M and N be Riemannian manifolds, N compact without boundary. We develop a definition of a variationally harmonic map (formula omitted) with respect to a general boundary condition of the kind (formula omitted), where (formula omitted) are given submanifolds depending smoothly on x. The given def...

Full description

Saved in:
Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 25; no. 4; pp. 409 - 429
Main Author Scheven, Christoph
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.04.2006
Subjects
Boundary conditions
Boundary layer
Calculus of variations
Harmonic analysis
Topological manifolds
Online AccessGet full text

Cover

More Information
Summary:Let M and N be Riemannian manifolds, N compact without boundary. We develop a definition of a variationally harmonic map (formula omitted) with respect to a general boundary condition of the kind (formula omitted), where (formula omitted) are given submanifolds depending smoothly on x. The given definition of variationally harmonic maps is slightly more restrictive, but also more natural than the usual definition of stationary harmonic maps. After deducing an energy monotonicity formula, it is possible to derive a regularity theory for variationally harmonic maps with general boundary data. The results include full boundary regularity in the Dirichlet boundary case gamma(x) = {g(x)} for (formula omitted) if N does not carry a nonconstant harmonic 2-sphere.[PUBLICATION ABSTRACT]
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-005-0329-6