An overview of unconstrained free boundary problems-Reference-Cited by-同舟云学术

An overview of unconstrained free boundary problems

Published:2015-09-13 Issue:2050 Volume:373 Page:20140281
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Figalli Alessio¹,Shahgholian Henrik²

Affiliation:

1. Department of Mathematics, The University of Texas at Austin, Austin, TX 78712-1202, USA

2. Department of Mathematics, KTH Royal Institute of Technology, Stockholm 100 44, Sweden

Abstract

In this paper, we present a survey concerning unconstrained free boundary problems of type where B 1 is the unit ball, Ω is an unknown open set, F 1 and F 2 are elliptic operators (admitting regular solutions), and

is a functions space to be specified in each case. Our main objective is to discuss a unifying approach to the optimal regularity of solutions to the above matching problems, and list several open problems in this direction.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2014.0281

Reference33 articles.

1. Graduate Studies in Mathematics, vol. 136;Petrosyan A,2012

2. The regularity of free boundaries in higher dimensions

3. The obstacle problem revisited

4. Graduate Studies in Mathematics, vol. 68;Caffarelli L,2005

5. Optimal Regularity for the No-Sign Obstacle Problem

Cited by 10 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A Nonconstant Gradient Constrained Problem for Nonlinear Monotone Operators;Axioms;2023-06-18

2. Lagrange multipliers and nonlinear variational inequalities with gradient constraints;Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences;2022-09-26

3. On the Existence of Radial Solutions to a Nonconstant Gradient-Constrained Problem;Symmetry;2022-07-11

4. Free boundary limit of a tumor growth model with nutrient;Journal de Mathématiques Pures et Appliquées;2021-11

5. Free boundary methods and non-scattering phenomena;Research in the Mathematical Sciences;2021-10-05