An overview of unconstrained free boundary problems | Zendy

Alessio Figalli | Zendy; Henrik Shahgholian | Zendy

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An overview of unconstrained free boundary problems

Author(s) -

Alessio Figalli,

Henrik Shahgholian

Publication year - 2015

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2014.0281

Subject(s) - boundary (topology) , computer science , mathematics , mathematical analysis

In this paper, we present a survey concerning unconstrained free boundary problems of type [Formula: see text] where B1 is the unit ball, Ω is an unknown open set, F(1) and F(2) are elliptic operators (admitting regular solutions), and [Formula: see text] 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.

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