Interfaces and Free Boundaries


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Volume 17, Issue 1, 2015, pp. 117–142
DOI: 10.4171/IFB/336

Published online: 2015-05-26

On the regularity of critical and minimal sets of a free interface problem

Nicola Fusco[1] and Vesa Julin[2]

(1) Università degli Studi di Napoli Federico II, Italy
(2) University of Jyväskylä, Finland

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].

Keywords: Free interface, regularity of minimal surfaces, Taylor cones

Fusco Nicola, Julin Vesa: On the regularity of critical and minimal sets of a free interface problem. Interfaces Free Bound. 17 (2015), 117-142. doi: 10.4171/IFB/336