© 2014

Semi-bounded Partial Differential Operators

  • 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 Operator Theory: Advances and Applications book series (OT, volume 243)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Alberto Cialdea, Vladimir Maz’ya
    Pages 1-28
  3. Alberto Cialdea, Vladimir Maz’ya
    Pages 73-92
  4. Alberto Cialdea, Vladimir Maz’ya
    Pages 93-135
  5. Alberto Cialdea, Vladimir Maz’ya
    Pages 137-143
  6. Alberto Cialdea, Vladimir Maz’ya
    Pages 145-167
  7. Alberto Cialdea, Vladimir Maz’ya
    Pages 169-242
  8. Back Matter
    Pages 243-252

About this book


This book examines the conditions for the semi-boundedness of partial differential operators, which are interpreted in different ways. For example, today we know a great deal about L2-semibounded differential and pseudodifferential operators, although their complete characterization in analytic terms still poses difficulties, even for fairly simple operators. In contrast, 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. This book works to address that gap. As such, various types of semi-boundedness are considered and a number of relevant conditions which are either necessary and sufficient or best possible in a certain sense are presented. The majority of the results reported on are the authors’ own contributions.


L^p-dissipativity elasticity system partial differential operators semi-boundedness weighted positivity

Authors and affiliations

  1. 1.Dept. of Mathematics, Computer Science and EconomicsUniversity of BasilicataPotenzaItaly
  2. 2.Linköping University Department of MathematicsLinköpingSweden

Bibliographic information

  • Book Title Semi-bounded Partial Differential Operators
  • Authors Alberto Cialdea
    Vladimir Maz'ya
  • Series Title Operator Theory: Advances and Applications
  • Series Abbreviated Title Operator Theory (Birkhäuser)
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-04557-3
  • Softcover ISBN 978-3-319-35670-9
  • eBook ISBN 978-3-319-04558-0
  • Series ISSN 0255-0156
  • Series E-ISSN 2296-4878
  • Edition Number 1
  • Number of Pages XIII, 252
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Operator Theory
    Partial Differential Equations
  • Buy this book on publisher's site


“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)