An optimal estimate for the singular set of a harmonic map in the free boundary.

Klaus Steffen; Frank Duzaar

Displaying similar documents to “An optimal estimate for the singular set of a harmonic map in the free boundary.”

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The boundary value problem for Dirac-harmonic maps

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Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian...

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Frank Duzaar, Andreas Gastel (1998)

Bollettino dell'Unione Matematica Italiana

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Studiamo le proprietà di regolarità delle mappe fra varietà di Riemann che minimizzano la $p$ -energia fra quelle che soddisfano una condizione di frontiera pazialmente libera. Proviamo che tali mappe sono Hölder continue vicino alla frontiera libera fuori di un insieme singolare, e otteniamo stime ottimali per la dimensione di Hausdorff di questo insieme singolare.