A local parabolic monotonicity formula on Riemannian manifolds
Eduardo. V. Teixeira, Lei Zhang
TL;DR
This paper develops a local parabolic almost monotonicity formula for two-phase free boundary problems on Riemannian manifolds, extending previous work to a more general geometric setting.
Contribution
It introduces a new monotonicity formula applicable to two-phase free boundary problems on Riemannian manifolds, broadening the scope of prior Euclidean results.
Findings
Established a local parabolic almost monotonicity formula on Riemannian manifolds.
Extended Euclidean free boundary analysis to curved geometric settings.
Provides tools for analyzing free boundary problems in Riemannian geometry.
Abstract
In this article we establish a local parabolic almost monotonicity formula for two phase free boundary problems on Riemannian manifolds, which is an extension of a work of Edquist-Petrosyan.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Numerical methods in inverse problems · Nonlinear Partial Differential Equations