Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45)

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis
Cover of the book Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) by Olivier Druet, Emmanuel Hebey, Frédéric Robert, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Olivier Druet, Emmanuel Hebey, Frédéric Robert ISBN: 9781400826162
Publisher: Princeton University Press Publication: January 10, 2009
Imprint: Princeton University Press Language: English
Author: Olivier Druet, Emmanuel Hebey, Frédéric Robert
ISBN: 9781400826162
Publisher: Princeton University Press
Publication: January 10, 2009
Imprint: Princeton University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Princeton University Press

Cover of the book The Source of the River by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book Wittgenstein Reads Freud by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book How to Do Things with Books in Victorian Britain by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book Noir Urbanisms by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book The Order of Terror by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book Mathematical Methods in Elasticity Imaging by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book Stealing Helen by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book The First Serious Optimist by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book On Bullshit by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book Why Everyone (Else) Is a Hypocrite by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book The Theory of Island Biogeography Revisited by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book Racial Justice in the Age of Obama by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book Plato's Democratic Entanglements by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book Foreign Direct Investment by Olivier Druet, Emmanuel Hebey, Frédéric Robert
Cover of the book The Battle for Yellowstone by Olivier Druet, Emmanuel Hebey, Frédéric Robert
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy