Energy minimizing harmonic maps with an obstacle at the free boundary |
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Authors: | Frank Duzaar Joseph F. Grotowski |
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Affiliation: | 1. FB Mathematil-Informatik/17, Universit?t-GH Paderborn, D-33095, Paderborn, Germany 2. Department of Mathematics and Statistics, Queen's University, K7L3N6, Kingston, Ont, Canada
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Abstract: | We consider partial regularity for energy minimizing maps satisfying a partially free boundary condition. This condition takes the form of the requirement that a relatively open subset of the boundary of the domain manifold be mapped into a closed submanifold with non-empty boundary, contained in the target manifold. We obtain an optimal estimate on the Hausdorff dimension of the singular set of such a map. Our result can be interpreted as regularity result for a vector-valued Signorini, or thin-obstacle, problem. |
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Keywords: | 58E20 58E35 49J40 |
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