A note on the monotonicity formula of Caffarelli-Jerison-Kenig∗
نویسنده
چکیده
The aim of this note is to prove the monotonicity formula of Caffarelli-Jerison-Kenig for functions, which are not necessarily continuous. We also give a detailed proof of the multiphase version of the monotonicity formula in any dimension.
منابع مشابه
Monotonicity Theorems for Laplace Beltrami Operator on Riemannian Manifolds
Abstract. 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 LaplaceBeltrami operator on Riemannian manifolds. As an application we show that our monotonicity theorems can be e...
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