Eduardo V Teixeira, Lei Zhang
Published 2008-12-01, updated 2009-06-10Version 3
For free boundary problems on Euclidean spaces, the monotonicity formulas of Alt-Caffarelli-Friedman and Caffarelli-Jerison-Kenig are cornerstones for the regularity theory as well as the existence theory. In this article we establish the analogs of these results for the Laplace-Beltrami operator on Riemannian manifolds. As an application we show that our monotonicity theorems can be employed to prove the Lipschitz continuity for the solutions of a general class of two-phase free boundary problems on Riemannian manifolds.
Residue-Torsion of the Laplacian on Riemannian Manifolds
Global Weak Rigidity of the Gauss-Codazzi-Ricci Equations and Isometric Immersions of Riemannian Manifolds with Lower Regularity
The Poisson equation on Riemannian manifolds with weighted Poincaré inequality at infinity
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