Regularity in free boundary problems

Claudia Lederman, Noemi Wolanski, Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem Gui-Qiang Chen, Mikhail Feldman, Free boundary problems and transonic shocks for the Euler equations in unbounded domains 11/07/2012 · Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems.

This book is concerned with several elliptic and parabolic obstacle-type problems with a focus on the cases where the free and fixed boundaries meet. The results presented complement those found in existing books in the subject, which mainly treat regularity properties away from the fixed boundary. 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.

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 ( …

Abstract. This thesis consists of three scientific papers, devoted to the regu-larity theory of free boundary problems. We use iteration arguments to derive the optimal regularity in the optimal switching problem, and to analyse the regularity of the free boundary in the biharmonic obstacle problem and in the double obstacle problem.In Paper A, we study the interior regularity of the solution

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