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Semi-bounded Differential Operators, Contractive Semigroups and Beyond

  • Book
  • © 2014

Overview

Authors:
  1. Alberto Cialdea

    1. Dept. of Mathematics, Computer Science and Economics, University of Basilicata, Potenza, Italy

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    You can also search for this author in PubMed   Google Scholar

  2. Vladimir Maz'ya

    1. Linköping University Department of Mathematics, Linköping, Sweden

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    You can also search for this author in PubMed   Google Scholar

  • Treatment of a subject that has hardly been worked in so far
  • No comparable book on the market, no significant intersections with existing monographic literature
  • Most results obtained by the authors themselves

Part of the book series: Operator Theory: Advances and Applications (OT, volume 243)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Preliminary Facts on Semi-boundedness of Forms and Operators

    • Alberto Cialdea, Vladimir Maz’ya
    Pages 1-28

  3. \(L^p\)-dissipativity of Scalar Second-order Operators with Complex Coefficients

    • Alberto Cialdea, Vladimir Maz’ya
    Pages 29-72

  4. Elasticity System

    • Alberto Cialdea, Vladimir Maz’ya
    Pages 73-92

  5. \(L^p\)-dissipativity for Systems of Partial Differential Operators

    • Alberto Cialdea, Vladimir Maz’ya
    Pages 93-135

  6. The Angle of \(L^p\)-dissipativity

    • Alberto Cialdea, Vladimir Maz’ya
    Pages 137-143

  7. Higher-order Differential Operators in \(L^p\)

    • Alberto Cialdea, Vladimir Maz’ya
    Pages 145-167

  8. Weighted Positivity and Other Related Results

    • Alberto Cialdea, Vladimir Maz’ya
    Pages 169-242

  9. Back Matter

    Pages 243-252
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Keywords

About this book

In the present book the conditions are studied for the semi-boundedness of partial differential operators which is interpreted in different ways. Nowadays one knows rather much about L2-semibounded differential and pseudo-differential operators, although their complete characterization in analytic terms causes difficulties even for rather simple operators. Until recently almost nothing was known about analytic characterizations of semi-boundedness for differential operators in other Hilbert function spaces and in Banach function spaces. The goal of the present book is to partially fill this gap. Various types of semi-boundedness are considered and some relevant conditions which are either necessary and sufficient or best possible in a certain sense are given. Most of the results reported in this book are due to the authors.

Reviews

“This book is valuable; it contains a lot of new information and deep, complicated proofs. … it is a very good book, and every serious research university library should get it. I expect it to inspire new research.” (Jerome A. Goldstein, Bulletin of the American Mathematical Society, Vol. 55 (1), January, 2018)


“The book is logically ordered and clearly written … . It will be of interest to specialists and graduate students working on partial differential operators in function spaces.” (Hector O. Fattorini, zbMATH 1317.47002, 2015)

Authors and Affiliations

  • Dept. of Mathematics, Computer Science and Economics, University of Basilicata, Potenza, Italy

    Alberto Cialdea

  • Linköping University Department of Mathematics, Linköping, Sweden

    Vladimir Maz'ya

Bibliographic Information

  • Book Title: Semi-bounded Differential Operators, Contractive Semigroups and Beyond

  • Authors: Alberto Cialdea, Vladimir Maz'ya

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-319-04558-0

  • Publisher: Birkhäuser Cham

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

  • Copyright Information: Springer International Publishing Switzerland 2014

  • Hardcover ISBN: 978-3-319-04557-3Published: 01 August 2014

  • Softcover ISBN: 978-3-319-35670-9Published: 23 August 2016

  • eBook ISBN: 978-3-319-04558-0Published: 21 July 2014

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XIII, 252

  • Topics: Operator Theory, Partial Differential Equations

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