Direct Epiperimetric Inequalities for the Thin Obstacle Problem and Applications

• Published in: Communications on pure and applied mathematics Vol. 73; no. 2; pp. 384 - 420
• Main Authors: Colombo, Maria, Spolaor, Luca, Velichkov, Bozhidar
• Format: Journal Article
• Language: English
• Published: New York John Wiley and Sons, Limited 01.02.2020; Wiley
• Subjects: Analysis of PDEs; Free boundaries; Inequality; Mathematics; Regularity

We introduce a new logarithmic epiperimetric inequality for the 2m‐Weiss energy in any dimension, and we recover with a simple direct approach the usual epiperimetric inequality for the 3/2‐Weiss energy. In particular, even in the latter case, unlike the classical statements, we do not assume any a...