Format:
Online-Ressource (X, 156 p. 119 illus., 1 illus. in color, online resource)
ISBN:
9783034803731
Series Statement:
Trends in Mathematics
Content:
Introduction -- On the Elements Involved in the Lack of Compactness in Critical Sobolev Embedding -- A Class of Second-order Dilation Invariant Inequalities -- Blow-up Solutions for Linear Perturbations of the Yamabe Equation -- Extremals for Sobolev and Exponential Inequalities in Hyperbolic Space -- The Lyapunov–Schmidt Reduction for Some Critical Problems -- A General Theorem for the Construction of Blowing-up Solutions to Some Elliptic Nonlinear Equations via Lyapunov–Schmidt’s Finite-dimensional Reduction -- Concentration Analysis and Cocompactness -- A Note on Non-radial Sign-changing Solutions for the Schrödinger–Poisson Problem in the Semiclassical Limit.
Content:
Concentration analysis provides, in settings without a priori available compactness, a manageable structural description for the functional sequences intended to approximate solutions of partial differential equations. Since the introduction of concentration compactness in the 1980s, concentration analysis today is formalized on the functional-analytic level as well as in terms of wavelets, extends to a wide range of spaces, involves much larger class of invariances than the original Euclidean rescalings and has a broad scope of applications to PDE. The book represents current research in concentration and blow-up phenomena from various perspectives, with a variety of applications to elliptic and evolution PDEs, as well as a systematic functional-analytic background for concentration phenomena, presented by profile decompositions based on wavelet theory and cocompact imbeddings.
Note:
Description based upon print version of record
,
IntroductionOn the Elements Involved in the Lack of Compactness in Critical Sobolev Embedding -- A Class of Second-order Dilation Invariant Inequalities -- Blow-up Solutions for Linear Perturbations of the Yamabe Equation -- Extremals for Sobolev and Exponential Inequalities in Hyperbolic Space -- The Lyapunov-Schmidt Reduction for Some Critical Problems -- A General Theorem for the Construction of Blowing-up Solutions to Some Elliptic Nonlinear Equations via Lyapunov-Schmidt’s Finite-dimensional Reduction -- Concentration Analysis and Cocompactness -- A Note on Non-radial Sign-changing Solutions for the Schrödinger-Poisson Problem in the Semiclassical Limit.
Additional Edition:
ISBN 9783034803724
Additional Edition:
Druckausg. Concentration analysis and applications to PDE Basel : Birkhäuser, 2013 ISBN 9783034803724
Language:
English
Subjects:
Mathematics
DOI:
10.1007/978-3-0348-0373-1
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Bookmarklink
