Emmanuele Dibenedetto, Ugo Pietro Gianazza, Vincenzo Vespri

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

• Format: PDF

Produktbeschreibung

Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete.

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The book is self-contained. Building on a similar monograph by the first author, the authors of the present book focus entirely on the Harnack estimates and on their applications: indeed a number of known regularity results are given a new proof, based on the Harnack inequality. It is 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.

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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)