Synopses & Reviews
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.
Review
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)
Synopsis
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.
Synopsis
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,
Synopsis
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,
Synopsis
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,
Table of Contents
Preface.- 1. Introduction.- 2. Preliminaries.- 3. Degenerate and Singular Parabolic Equations.- 4.