Proves existence of minimizers together with optimal Lipschitz regularity of the functions and analytic regularity of the free boundaries away from a codimension-2 singular set for two semilinear variational problems with topological constraints.
Plateau borders in soap films and G auss' capillarity theory
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Free boundary regularity for semilinear variational problems with a topological constraint
Proves existence of minimizers together with optimal Lipschitz regularity of the functions and analytic regularity of the free boundaries away from a codimension-2 singular set for two semilinear variational problems with topological constraints.