Some remarks on stability of cones for the one-phase free boundary problem

By David Jerison, Ovidiu Savin. 2014

108 citations recorded by the source corpus.

We show that stable cones for the one-phase free boundary problem are hyperplanes in dimension 4. As a corollary, both one and two-phase energy minimizing hypersurfaces are smooth in dimension 4.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/da5943275394463cec6179f8522c2b11fc2c9a39

Citations in the corpus

• A minimization problem with free boundary related to a cooperative system (2016, unknown): “Let us note that by [8, 12, 14] it is known that 5 ≤ k∗ ≤ 7.”