A boundary monotonicity inequality for variationally biharmonic maps and applications to regularity theory
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.
KeywordsBiharmonic maps Boundary monotonicity inequality Regularity
I would like to thank Prof. Dr. Christoph Scheven for his much helpful advice.
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