Regularity in free boundary problems

26/04/2018 · The main mathematical challenge is understanding the regularity of free boundaries. The obstacle problem is the most classical and motivating example in the study of free boundary problems. REGULARITY OF THE FREE BOUNDARY FOR THE VECTORIAL BERNOULLI PROBLEM DARIO MAZZOLENI, SUSANNA TERRACINI, BOZHIDAR VELICHKOV Abstract. In this paper we study the regularity of the free boundary for a vector-valued Bernoulli problem, with no sign assumptions on the boundary data. More precisely, given an open, smooth set of nite measure D ˆRd

Title: An epiperimetric inequality for the regularity of some free boundary problems: the $2$-dimensional case Authors: Luca Spolaor , Bozhidar Velichkov (Submitted on 6 Dec 2016 ( …

FREE BOUNDARY REGULARITY PROBLEMS T. TORO In the 1980’s Alt-Ca arelli and Alt-Ca arilly-Friedman initiated the study of minimizing problems with free boundary, since then this eld as boomed. In this situation the minimizer satis es a PDE, and the central question … Title: An epiperimetric inequality for the regularity of some free boundary problems: the $2$-dimensional case Authors: Luca Spolaor , Bozhidar Velichkov (Submitted on 6 Dec 2016 ( …

Two-phase problems with distributed sources: regularity of the free boundary De Silva, Daniela, Ferrari, Fausto, and Salsa, Sandro, Analysis & PDE, 2014; An unstable elliptic free boundary problem arising in solid combustion Monneau, R. and Weiss, G. S., Duke Mathematical Journal, 2007

We provide a rather complete description of the sharp regularity theory to a family of heterogeneous, two-phase free boundary problems, J γ → min, ruled by nonlinear, p-degenerate elliptic operators.Included in such family are heterogeneous cavitation problems of Prandtl–Batchelor type, singular degenerate elliptic equations; and obstacle type systems. Regularity in free boundary problems Kinderlehrer, D. ; Nirenberg, L. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze , Série 4 , Tome 4 (1977) no. 2 , p. 373-391