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Lecture Notes in Mathematics

Free Boundary Problems

Regularity Properties Near the Fixed Boundary

Authors: Apushkinskaya, Darya

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  • Presents obstacle-type problems in the parabolic case, not just the elliptic case
  • Focuses on the cases where the free and fixed boundaries meet
  • Several appendices provide the reader with a detailed exposition of the deep techniques of the theory
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  • ISBN 978-3-319-97079-0
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About this book

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 $C^1$-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.

About the authors

Darya Apushkinskaya received her PhD degree from St. Petersburg State University and her Habilitation from Saarland University. Her research includes problems in non-smooth domains for equations with singular coefficients, variational problems with non-standard growth conditions, error analysis for solutions of variational and nonvariational problems and, of course,  free boundary problems and their applications to biology and solid state physics.

Table of contents (3 chapters)

Table of contents (3 chapters)
  • Introduction

    Pages 1-27

    Apushkinskaya, Darya

  • No-Sign Parabolic Obstacle-Type Problems

    Pages 29-71

    Apushkinskaya, Darya

  • Boundary Estimates for Solutions of Free Boundary Problems

    Pages 73-106

    Apushkinskaya, Darya

Buy this book

eBook $19.99
$39.99 (listprice)
price for USA in USD (gross)
valid through July 31, 2020
  • ISBN 978-3-319-97079-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $29.99
$49.99 (listprice)
price for USA in USD
valid through July 31, 2020
  • ISBN 978-3-319-97078-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Free Boundary Problems
Book Subtitle
Regularity Properties Near the Fixed Boundary
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2218
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-97079-0
DOI
10.1007/978-3-319-97079-0
Softcover ISBN
978-3-319-97078-3
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVII, 146
Number of Illustrations
10 illustrations in colour
Topics

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