Moving Interfaces and Quasilinear Parabolic Evolution Equations, Pr?ss

Автор: Emmanuele DiBenedetto; Prof. Ugo Pietro Gianazza U
Название: Harnack`s Inequality for Degenerate and Singular Parabolic Equations
ISBN: 1489999760 ISBN-13(EAN): 9781489999764
Издательство: Springer
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Цена: 16769.00 р.
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Описание:

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.

It seemed therefore timely to trace a comprehensive overview, that would highlight the main issues and also the problems that still remain open. The authors give a comprehensive treatment of the Harnack inequality for non-negative solutions to p-laplace and porous medium type equations, both in the degenerate (p>2 or m>1) and in the singular range (1pmThe 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.