Advances in Partial Differential Equations

Parabolicity, Volterra Calculus, and Conical Singularities

A Volume of Advances in Partial Differential Equations

Editors: Albeverio, S., Demuth, M., Schrohe, E., Schulze, B.-W. (Eds.)

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About this book

Partial differential equations constitute an integral part of mathematics. They lie at the interface of areas as diverse as differential geometry, functional analysis, or the theory of Lie groups and have numerous applications in the applied sciences. A wealth of methods has been devised for their analysis. Over the past decades, operator algebras in connection with ideas and structures from geometry, topology, and theoretical physics have contributed a large variety of particularly useful tools. One typical example is the analysis on singular configurations, where elliptic equations have been studied successfully within the framework of operator algebras with symbolic structures adapted to the geometry of the underlying space. More recently, these techniques have proven to be useful also for studying parabolic and hyperbolic equations. Moreover, it turned out that many seemingly smooth, noncompact situations can be handled with the ideas from singular analysis. The three papers at the beginning of this volume highlight this aspect. They deal with parabolic equations, a topic relevant for many applications. The first article prepares the ground by presenting a calculus for pseudo differential operators with an anisotropic analytic parameter. In the subsequent paper, an algebra of Mellin operators on the infinite space-time cylinder is constructed. It is shown how timelike infinity can be treated as a conical singularity.

Table of contents (5 chapters)

  • Volterra Families of Pseudodifferential Operators

    Krainer, Thomas

    Pages 1-45

  • The Calculus of Volterra Mellin Pseudodifferential Operators with Operator-valued Symbols

    Krainer, Thomas

    Pages 47-91

  • On the Inverse of Parabolic Systems of Partial Differential Equations of General Form in an Infinite Space-Time Cylinder

    Krainer, Thomas (et al.)

    Pages 93-278

  • On the Factorization of Meromorphic Mellin Symbols

    Witt, Ingo

    Pages 279-306

  • Coordinate Invariance of the Cone Algebra with Asymptotics

    Kapanadze, D. (et al.)

    Pages 307-358

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0348-8191-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-0348-9469-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Parabolicity, Volterra Calculus, and Conical Singularities
Book Subtitle
A Volume of Advances in Partial Differential Equations
Editors
  • Sergio Albeverio
  • Michael Demuth
  • Elmar Schrohe
  • Bert-Wolfgang Schulze
Series Title
Advances in Partial Differential Equations
Series Volume
138
Copyright
2002
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8191-3
DOI
10.1007/978-3-0348-8191-3
Softcover ISBN
978-3-0348-9469-2
Edition Number
1
Number of Pages
XI, 359
Topics