Blow up theory for elliptic pdes in riemannian geometry mn 45

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This work develops critical new ideas and methods for the analysis of elliptic PDEs on compact Riemannian manifolds, especially in the framework of the Yamabe equation, critical Sobolev embedding and blow-up techniques (asymptotic analysis).



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 Schrodinger 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.

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Taal: en

Bindwijze: Paperback

Oorspronkelijke releasedatum: 09 mei 2004

Aantal pagina's: 224

Illustraties: Nee

Hoofdauteur: Olivier Druet

Tweede Auteur: Emmanuel Hebey

Co Auteur: Frederic Robert

Hoofduitgeverij: Princeton University Press

Editie: New title

Extra groot lettertype: Nee

Product breedte: 159 mm

Product hoogte: 25 mm

Product lengte: 241 mm

Studieboek: Ja

Verpakking breedte: 152 mm

Verpakking hoogte: 235 mm

Verpakking lengte: 235 mm

Verpakkingsgewicht: 312 g

EAN: 9780691119533

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