Concentration analysis and applications to PDE
by Adimurthi Sandeep, K. Schindler, Ian Tintarev, Kyril
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 …
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- Full title :Concentration analysis and applications to PDE / Adimurthi, K. Sandeep, Ian Schindler, Cyril Tintarev, editors.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2013.
Publication Statements
- Publisher(s):Birkhäuser
- Place of Publication:Basel
- Language:eng
- Publication Date:2013.
The Physical Object
- Description:1 online resource
Edition Identifiers
- ISBN:9783034803731, 3034803737
- oclc:ocn864305212
- LC Classification:QA377
- Dewey Decimal:515.353
Table of Contents
On the elements involved in the lack of compactness in critical Sobolev embedding / H. Bahouri -- A class of second-order dilation invariant inequalities / P. Caldiroli and R. Musina -- Blow-up solutions for linear perturbations of the Yamabe equation / P. Esposito, A. Pistoia and J. Vetois -- Extremals for Sobolev and exponential inequalities in hyperbolic space / G. Mancini and K. Sandeep -- The Ljapunov-Schmidt reduction for some critical problems / A. Pistoia -- A general theorem for the construction of blowing-up solutions to some elliptic nonlinear equations via Lyapunov-Schmidt's finite-dimensional reduction / F. Robert and J. Vetois -- Concentration analysis and cocompactness / C. Tintarev -- A note on non-radial sign-changing solutions for the Schrodinger-Poisson problem in the semiclassical limit / G. Vaira.
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