An Epiperimetric Inequality for the Regularity of Some Free Boundary Problems: The 2‐Dimensional Case
An Epiperimetric Inequality for the Regularity of Some Free Boundary Problems: The 2‐Dimensional Case
Abstract Using a direct approach, we prove a two‐dimensional epiperimetric inequality for the one‐phase problem in the scalar and vectorial cases and for the double‐phase problem. From this we deduce, in dimension 2, the C 1,α regularity of the free boundary in the scalar one‐phase and double‐phase problems, and of …