Revista Matemática Iberoamericana
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Published online: 2012-07-16
An elliptic variational problem involving level surface area on Riemannian manifoldsEduardo V. Teixeira and Lei Zhang (1) Universidade Federal do Ceará, Fortaleza, Brazil
(2) University of Florida, Gainesville, USA
We study a variational problem involving a Dirichlet integral and the area of a level surface on arbitrary $n$-dimensional Riemannian manifolds. We prove optimal regularity results for minimizers and derive a jump condition along the level surface. We also obtain smoothness of the interface up to a small singular set of Hausdorff dimension less then or equal to $n-8$.
Keywords: Monotonicity formula, variational form, free boundary problems
Teixeira Eduardo, Zhang Lei: An elliptic variational problem involving level surface area on Riemannian manifolds. Rev. Mat. Iberoam. 28 (2012), 759-772. doi: 10.4171/RMI/690