On the regularity of critical and minimal sets of a free interface problem
Nicola Fusco, Vesa Julin · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2015
We study a free interface problem of finding the optimal energy configuration for mixtures of two conducting materials with an additional perimeter penalization of the interface. We employ the regularity theory of linear elliptic equations to study the possible opening angles of Taylor cones and to give a different proof of a partial regularity result by Fan Hua Lin [15].