Ugo Pietro Gianazza – författare

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 (1

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 (1<p<2 or 0<m<1), starting from the notion of solution and building all the necessary technical tools.

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.

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 (1

This volume is a selection of contributions offered by friends, collaborators, past students in memory of Enrico Magenes. The first part gives a wide historical perspective of Magenes' work in his 50-year mathematical career; the second part contains original research papers, and shows how ideas, methods, and techniques introduced by Magenes and his collaborators still have an impact on the current research in Mathematics.

This volume is a selection of contributions offered by friends, collaborators, past students in memory of Enrico Magenes. The first part gives a wide historical perspective of Magenes'' work in his 50-year mathematical career; the second part contains original research papers, and shows how ideas, methods, and techniques introduced by Magenes and his collaborators still have an impact on the current research in Mathematics.