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

  • Serdar Altuntas


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.


Biharmonic maps Boundary monotonicity inequality Regularity 



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


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Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität Duisburg-EssenEssenGermany

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