Isolated Singularities in Partial Differential Inequalities
Isolated Singularities in Partial Differential Inequalities
$160.00
USDIn 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
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
Product details
January 2016Adobe eBook Reader
9781316496893
0 pages
0kg
4 b/w illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- Preface
- 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
- Bibliography
- Index.
