Mathematical notes 45 blow up theory for elliptic pdes in riemannian geometry
Direct beschikbaar
Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand side and a critical nonlinearity on the right hand side.
A significant development in the study of such equations occurred in the 1980s. It was discovered that the sequence splits into a solution of the limit equation--a finite sum of bubbles--and a rest that converges strongly to zero in the Sobolev space consisting of square integrable functions whose gradient is also square integrable. This splitting is known as the integral theory for blow-up. In this book, the authors develop the pointwise theory for blow-up. They introduce new ideas and methods that lead to sharp pointwise estimates. These estimates have important applications when dealing with sharp constant problems (a case where the energy is minimal) and compactness results (a case where the energy is arbitrarily large). The authors carefully and thoroughly describe pointwise behavior when the energy is arbitrary.
Intended to be as self-contained as possible, this accessible book will interest graduate students and researchers in a range of mathematical fields.
- 1 Bekijk alle specificaties
Taal: en
Bindwijze: E-book
Oorspronkelijke releasedatum: 10 januari 2009
Aantal pagina's: 224
Ebook Formaat: Adobe ePub
Illustraties: Nee
Hoofdauteur: Olivier Druet
Tweede Auteur: Emmanuel Hebey
Co Auteur: Frederic Robert
Hoofduitgeverij: Princeton University Press
Lees dit ebook op: Android (smartphone en tablet)
Lees dit ebook op: Kobo e-reader
Lees dit ebook op: Desktop (Mac en Windows)
Lees dit ebook op: iOS (smartphone en tablet)
Lees dit ebook op: Windows (smartphone en tablet)
Product breedte: 159 mm
Product hoogte: 25 mm
Product lengte: 241 mm
Studieboek: Ja
Verpakking hoogte: 25 mm
EAN: 9781400826162