Blow-up theory for elliptic PDEs in Riemannian geometry / Olivier Druet, Emmanuel Hebey, Frédéric Robert.

By:

Druet, Olivier, 1976-

Contributor(s):

Material type: Text

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781400826162
1400826160
1282087231
9781282087231
1282935372
9781282935372
9786612935374
6612935375
9786612087233
6612087234

Subject(s): Genre/Form:

Additional physical formats: Print version:: Blow-up theory for elliptic PDEs in Riemannian geometry.DDC classification:

515/.353 22

LOC classification:

QA315 .D78 2004eb

Other classification:

31.45

Online resources:

Click here to access online

Contents:

Preface; Chapter 1. Background Material; Chapter 2. The Model Equations; Chapter 3. Blow-up Theory in Sobolev Spaces; Chapter 4. Exhaustion and Weak Pointwise Estimates; Chapter 5. Asymptotics When the Energy Is of Minimal Type; Chapter 6. Asymptotics When the Energy Is Arbitrary; Appendix A. The Green's Function on Compact Manifolds; Appendix B. Coercivity Is a Necessary Condition; Bibliography

Summary: 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 s.

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Includes bibliographical references (pages 213-218).

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 s.