tailieunhanh - Báo cáo hóa học: " Editorial Harnack’s Estimates: Positivity and Local Behavior of Degenerate and Singular Parabolic Equations"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Editorial Harnack’s Estimates: Positivity and Local Behavior of Degenerate and Singular Parabolic Equations | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 42548 5 pages doi 2007 42548 Editorial Harnack s Estimates Positivity and Local Behavior of Degenerate and Singular Parabolic Equations Emmanuele DiBenedetto Ugo Gianazza Mikhail Safonov Jose Miguel Urbano and Vincenzo Vespri Received 20 November 2006 Accepted 28 November 2006 Copyright 2007 Emmanuele DiBenedetto et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. The subject of Harnack s inequalities and more generally of regularity estimates for degenerate and singular elliptic and parabolic equations has developed considerably in recent years in many unexpected and challenging directions therefore it seemed timely to trace an overview that would highlight emerging trends and issues of this fascinating research topic. This special issue is an outgrowth of a Summer School that took place in Cortona Italy in Summer 2005 and builds on the recent developments that were presented at that meeting and on the ones that followed soon after. The editors took the opportunity kindly offered by the BVP editor-in-chief to record this momentous series of events into an issue that would emphasize and stress the importance of this kind of research both in terms of its intrinsic results and the new techniques it offers in classical analysis. The relevance of Harnack s estimates has been brought to light by the recent Perelman s solution of the Poincare conjecture which ultimately relies on a Harnack estimate. The editors aimed at a volume that might serve as a reference point in the field and as a source of inspiration for young researchers therefore collecting cutting-edge original and unpublished research articles. The opening contribution by Kassmann is a survey on the main results and applications of the Harnack inequality. The .