Emmanuele Dibenedetto, Ugo Pietro Gianazza, Vincenzo Vespri

Harnack's Inequality for Degenerate and Singular Parabolic Equations (eBook, PDF)

• Format: PDF

Produktbeschreibung

While degenerate and singular parabolic equations have been researched extensively for the last 25 years, the Harnack inequality for nonnegative solutions to these equations has received relatively little attention. Recent progress has been made on the Harnack inequality to the point that the theory is now reasonably complete-except for the singular subcritical range-both for the p-Laplacian and the porous medium equations.

This monograph provides a comprehensive overview of the subject that highlights open problems. The authors treat the Harnack inequality for nonnegative solutions to p-Laplace and porous medium type equations, both in the degenerate and in the singular range. The work is mathematical in nature; its aim is to introduce a novel set of tools and techniques that deepen our understanding of the notions of degeneracy and singularity in partial differential equations.

Although related in spirit to a monograph by the first author in this subject, this book is a self-contained treatment with a different perspective. Here the focus is entirely on the Harnack estimates and on their applications; the authors use the Harnack inequality to reprove a number of known regularity results. This book is aimed at researchers and advanced graduate students who work in this fascinating field.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer New York
• Seitenzahl: 278
• Erscheinungstermin: 13. November 2011
• Englisch
• ISBN-13: 9781461415848
• Artikelnr.: 37356937

Inhaltsangabe

Preface.- 1. Introduction.- 2. Preliminaries.- 3. Degenerate and Singular Parabolic Equations.- 4. Expansion of Positivity.- 5. The Harnack Inequality for Degenerate Equations.- 6. The Harnack Inequality for Singular Equations.- 7. Homogeneous Monotone Singular Equations.- Appendix A.- Appendix B.- Appendix C.- References.- Index.

Rezensionen

From the reviews: "Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years, but the issue of the Harnack inequality has remained basically open. In the Introduction to this monograph, the authors present the history of the subject beginning with Harnack's inequality for nonnegative harmonic functions ... . The book is self-contained and addressed to all professionals active in the field, and also to advanced graduate students interested in understanding the main issues of this fascinating research field." (Boris V. Loginov, Zentralblatt MATH, Vol. 1237, 2012)