Free Boundary Problems

Regularity Properties Near the Fixed Boundary

  • Darya Apushkinskaya

Part of the Lecture Notes in Mathematics book series (LNM, volume 2218)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Darya Apushkinskaya
    Pages 1-27
  3. Darya Apushkinskaya
    Pages 29-71
  4. Back Matter
    Pages 107-146

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.


Contact Points Global Solutions Monotonicity Formulas Parabolic Free Boundary Problems Quadratic Growth Estimates Regularity

Authors and affiliations

  • Darya Apushkinskaya
    • 1
  1. 1.Department of MathematicsSaarland UniversitySaarbrückenGermany

Bibliographic information