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Regularity Estimates for Nonlinear Elliptic and Parabolic Problems

Cetraro, Italy 2009

  • Book
  • © 2012

Overview

Authors:
  1. John Lewis

    1. , Mathematics Department, University of Kentucky, Lexington, USA

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  2. Peter Lindqvist

    1. of Science and Technology, Department of Mathematical Sciences, Norwegian Universitiy, Trondheim, Norway

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  3. Juan J. Manfredi

    1. Department of Mathematics, University of Pittsburgh, Pittsburgh, USA

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  4. Sandro Salsa

    1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

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  • The notes trace a timely overview of the main issues in the regularity theory for degenerate and singular elliptic and parabolic PDEs
  • The deep connections among seemingly unrelated topics are shown
  • The main results are thoroughly discussed and proper counterexamples are presented
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2045)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xi
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  2. Applications of Boundary Harnack Inequalities for p Harmonic Functions and Related Topics

    • J. Lewis
    Pages 1-72

  3. Regularity of Supersolutions

    • Peter Lindqvist
    Pages 73-131

  4. Introduction to Random Tug-of-War Games and PDEs

    • Juan J. Manfredi
    Pages 133-151

  5. The Problems of the Obstacle in Lower Dimension and for the Fractional Laplacian

    • Sandro Salsa
    Pages 153-244

  6. Back Matter

    Pages 245-247
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Keywords

About this book

The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful research field. In particular considerable strides have been made in regularity estimates for degenerate and singular elliptic and parabolic equations over the last several years, and in many unexpected and challenging directions. Because of all these recent results, it seemed high time to create an overview that would highlight emerging trends and issues in this fascinating research topic in a proper and effective way. The course aimed to show the deep connections between these topics and to open new research directions through the contributions of leading experts in all of these fields.

Authors and Affiliations

  • , Mathematics Department, University of Kentucky, Lexington, USA

    John Lewis

  • of Science and Technology, Department of Mathematical Sciences, Norwegian Universitiy, Trondheim, Norway

    Peter Lindqvist

  • Department of Mathematics, University of Pittsburgh, Pittsburgh, USA

    Juan J. Manfredi

  • Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Sandro Salsa

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