Free boundary regularity for surfaces minimizing

Author:
Edith A. Cook

Journal:
Trans. Amer. Math. Soc. **290** (1985), 503-526

MSC:
Primary 49F22

MathSciNet review:
792809

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Abstract: In , fix a hyperplane and -dimensional surface lying to one side of with boundary in . We prove the existence of and minimizing among all -dimensional having boundary , where is a free boundary constrained to lie in . We prove that except possibly on a set of Hausdorff dimension , is locally a manifold with boundary for . If , is replaced by real analytic.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1985-0792809-6

Keywords:
Free boundary,
variational problem,
flat chains,
varifold,
elliptic PDE,
complementing boundary condition

Article copyright:
© Copyright 1985
American Mathematical Society