Free boundary problems : regularity properties near the fixed boundary /

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Bibliographic Details
Author / Creator:	Apushkinskaya, Darya, author.
Imprint:	Cham, Switzerland : Springer, 2018.
Description:	1 online resource (xvii, 146 pages) : color illustrations.
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 2218 Lecture notes in mathematics (Springer-Verlag) ; 2218.
Subject:	Boundary value problems. Boundary value problems. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11706271

Hidden Bibliographic Details
ISBN:	9783319970790 3319970798 9783319970783 331997078X 9783319970806 3319970801
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed September 26, 2018).
Summary:	"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. The topics include optimal regularity, analysis of global solutions, tangential touch of the free and fixed boundaries, as well as Lipschitz- and C¹-regularity of the free boundary. Special attention is given to local versions of various monotonicity formulas. The intended audience includes research mathematicians and advanced graduate students interested in problems with free boundaries"--Print version, page 4 of cover.
Other form:	Print version: Apushkinskaya, Darya. Free boundary problems. Cham, Switzerland : Springer, [2018] 9783319970783
Standard no.:	10.1007/978-3-319-97079-0 10.1007/978-3-319-97

Table of Contents:

Introduction: No-sign parabolic obstacle-type problems
Boundary estimates for solutions of free boundary problems
Appendices
Notes
Open problems
No-sign parabilic obstacle-type problems: Statement of the problem and main results
Optimal regularity of solutions
Useful properties of solutions
Classification of the nonnegative global solutions
Geometric classification of the global solutions with no sign restrictions
Characterization of the free boundary points newar [Pi]
Regularity properties of solutions
Regularity properties of the free boundary
Boundary estimates for solutions of free boundary problems: One-sided estimates up to the boundary for solutions to the elliptic obstacle problem
Boundary estimates for solutions to the two-phase elliptic problem
Estimates near the given boundary of the second-order derivatives for solutions to the two-phase parabolic problem
Uniform estimates near the initial stata for solutions to the two-phase parabolic problem
Monotonicity formulas
Auxiliary results
Additional facts.

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