Compactness and stability for nonlinear elliptic equations / Emmanuel Hebey.

Format:

Book

Author/Creator:

Hebey, Emmanuel, 1964-

Contributor:

Rosengarten Family Fund.

Series:

Zurich lectures in advanced mathematics

Language:

English

Subjects (All):

Differential equations, Elliptic.

Manifolds (Mathematics).

Differential equations, Nonlinear.

Physical Description:

x, 291 pages ; 24 cm.

Place of Publication:

Zürich, Switzerland : European Mathematical Society, [2014]

Summary:

The book offers an expanded version of lectures given at ETH Zürich in the framework of a Nachdiplomvorlesung. Compactness and stability for nonlinear elliptic equations in the inhomogeneous context of closed Riemannian manifolds are investigated, a field presently undergoing great development. The author describes blow-up phenomena and presents the progress made over the past years on the subject, giving an up-to-date description of the new ideas, concepts, methods, and theories in the field. Special attention is devoted to the nonlinear stationary Schrödinger equation and to its critical formulation. Intended to be as self-contained as possible, the book is accessible to a broad audience of readers, including graduate students and researchers.

Contents:

1. Some model equations

2. Basic variational methods

3. The L [superscript] p and H¹-theories for blow-up

4. Blowing-up solutions in the critical case

5. An introduction to elliptic stability

6. Bounded stability

7. The C⁰-theory for blow-up

8. Analytic stability.

Notes:

University lectures.

Includes bibliographical references (pages 285-291).

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

9783037191347

3037191341

OCLC:

889706814

Publisher Number:

99996450699