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Isolated Singularities in Partial Differential Inequalities


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: February 2016
  • availability: Available
  • format: Hardback
  • isbn: 9781107138384

£ 116.00

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About the Authors
  • In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the simplest way to study an equation is often to study a corresponding inequality; for example, using sub and superharmonic functions to study harmonic functions. Another unusual feature of the present book is that it is based on integral representation formulae and nonlinear potentials, which have not been widely investigated so far. This approach can also be used to tackle higher order differential equations. The book will appeal to graduate students interested in analysis, researchers in pure and applied mathematics, and engineers who work with partial differential equations. Readers will require only a basic knowledge of functional analysis, measure theory and Sobolev spaces.

    • Describes various methods developed by the authors in the study of isolated singularities
    • Self-contained chapters give readers quick access to specific mathematical methods
    • Each chapter concludes with historical notes and pointers to related literature
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    Reviews & endorsements

    'The book is well written and provides for attractive reading on the subject, acquainting the reader with various properties of differential inequalities and their solutions.' Michael Ruzhansky, MathSciNet

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    Product details

    • Date Published: February 2016
    • format: Hardback
    • isbn: 9781107138384
    • length: 362 pages
    • dimensions: 240 x 165 x 27 mm
    • weight: 0.73kg
    • contains: 4 b/w illus.
    • availability: Available
  • Table of Contents

    1. Representation formulae
    2. Isolated singularities of nonlinear elliptic inequalities
    3. More on isolated singularities for semilinear elliptic inequalities
    4. Elliptic inequalities for the Laplace operator with Hardy potential
    5. Singular solutions for nondivergence type elliptic inequalities
    6. Isolated singularities of polyharmonic inequalities
    7. Nonlinear biharmonic inequalities
    8. Initial blow-up for nonlinear parabolic inequalities
    9. Semilinear elliptic systems of differential inequalities
    10. Isolated singularities for nonlocal elliptic systems
    11. Isolated singularities for systems of parabolic inequalities
    Appendix A. Estimates for the heat kernel
    Appendix B. Heat potential estimates
    Appendix C. Nonlinear potential estimates

  • Authors

    Marius Ghergu, University College Dublin
    Marius Ghergu is a Lecturer in the School of Mathematical Sciences at University College Dublin, Ireland.

    Steven D. Taliaferro, Texas A & M University
    Steven D. Taliaferro is Associate Professor in the Department of Mathematics at Texas A & M University.

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