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Regularity of the One-phase Free Boundaries

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  • Open Access
  • © 2023

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Overview

  • This book is open access, which means that you have free and unlimited access
  • Winner of the 2019 Book Prize of the Unione Matematica Italiana
  • Freely available to all readers, this book is open access
  • Provides a comprehensive and self-contained Introduction to the free boundary regularity theory

Part of the book series: Lecture Notes of the Unione Matematica Italiana (UMILN, volume 28)

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Table of contents (12 chapters)

Keywords

About this book

This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research. 


The exposition is organized around four main theorems, which are dedicated to the one-phase functional in its simplest form. Many of the methods and the techniques presented here are very recent and were developed in the context of different free boundary problems. We also give the detailed proofs of several classical results, which are based on some universal ideas and are recurrent in the free boundary, PDE and the geometric regularity theories.


This book is aimed at graduate students and researches and is accessible to anyone with a moderate level of knowledge of elliptical PDEs.

Authors and Affiliations

  • Department of Mathematics, University of Pisa, Pisa, Italy

    Bozhidar Velichkov

About the author

Bozhidar Velichkov is working in the fields of Calculus of Variations and Partial Differential Equations, in particular, his research is focused on the regularity and the local structure of the solutions to free boundary problems. He has several important contributions to the theory of the vectorial free boundary problems and developed new tools as the epiperimetric and the log-epiperimetric inequalities for free boundary problems.



Bibliographic Information

  • Book Title: Regularity of the One-phase Free Boundaries

  • Authors: Bozhidar Velichkov

  • Series Title: Lecture Notes of the Unione Matematica Italiana

  • DOI: https://doi.org/10.1007/978-3-031-13238-4

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s) 2023

  • Softcover ISBN: 978-3-031-13237-7Published: 25 February 2023

  • eBook ISBN: 978-3-031-13238-4Published: 24 February 2023

  • Series ISSN: 1862-9113

  • Series E-ISSN: 1862-9121

  • Edition Number: 1

  • Number of Pages: XIII, 247

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Optimization, Analysis

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