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p-Laplace Equation in the Heisenberg Group

Regularity of Solutions

  • Book
  • © 2015

Overview

Authors:
  1. Diego Ricciotti

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

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  • Accessible to students at the graduate level
  • Presents the basic properties of the Heisenberg group in self-contained coverage
  • Allows the reader to focus on the core of the theory and techniques in the field
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction

    • Diego Ricciotti
    Pages 1-6

  3. The Heisenberg Group

    • Diego Ricciotti
    Pages 7-26

  4. The p-Laplace Equation

    • Diego Ricciotti
    Pages 27-42

  5. \(C^\infty \) Regularity for the Non-degenerate Equation

    • Diego Ricciotti
    Pages 43-61

  6. Lipschitz Regularity

    • Diego Ricciotti
    Pages 63-85

  7. Back Matter

    Pages 87-87
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Keywords

About this book

This works focuses on regularity theory for solutions to the p-Laplace equation in the Heisenberg group. In particular, it presents detailed proofs of smoothness for solutions to the non-degenerate equation and of Lipschitz regularity for solutions to the degenerate one. An introductory chapter presents the basic properties of the Heisenberg group, making the coverage self-contained. The setting is the first Heisenberg group, helping to keep the notation simple and allow the reader to focus on the core of the theory and techniques in the field. Further, detailed proofs make the work accessible to students at the graduate level.

Authors and Affiliations

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

    Diego Ricciotti

Bibliographic Information

  • Book Title: p-Laplace Equation in the Heisenberg Group

  • Book Subtitle: Regularity of Solutions

  • Authors: Diego Ricciotti

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-23790-9

  • Publisher: Springer Cham

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

  • Copyright Information: The Author(s) 2015

  • Softcover ISBN: 978-3-319-23789-3Published: 06 January 2016

  • eBook ISBN: 978-3-319-23790-9Published: 28 December 2015

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: XIV, 87

  • Topics: Ordinary Differential Equations

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