A boundary monotonicity inequality for variationally biharmonic maps and applications to regularity theory

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Abstract

We derive a boundary monotonicity formula for a class of biharmonic maps with Dirichlet boundary conditions. A monotonicity formula is crucial in the theory of partial regularity in supercritical dimensions. As a consequence of such a boundary monotonicity formula, one is able to show partial regularity for variationally biharmonic maps and full boundary regularity for minimizing biharmonic maps.

Keywords

Biharmonic maps Boundary monotonicity inequality Regularity 

Notes

Acknowledgements

I would like to thank Prof. Dr. Christoph Scheven for his much helpful advice.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität Duisburg-EssenEssenGermany

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