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Title Concentration analysis and applications to PDE : ICTS Workshop, Bangalore, January 2012 / Adimurthi, K. Sandeep, Ian Schindler, Kyril Tintarev, editors
Published Basel : Birkhäuser, 2013
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Description 1 online resource
Series Trends in mathematics
Trends in mathematics.
Contents 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 LyapunovSchmidt Reduction for Some Critical Problems -- A General Theorem for the Construction of Blowing-up Solutions to Some Elliptic Nonlinear Equations via LyapunovSchmidts Finite-dimensional Reduction -- Concentration Analysis and Cocompactness -- A Note on Non-radial Sign-changing Solutions for the SchrdingerPoisson Problem in the Semiclassical Limit
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
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Subject Differential equations, Partial -- Congresses.
Embeddings (Mathematics) -- Congresses.
Genre/Form Conference papers and proceedings.
Conference papers and proceedings.
Form Electronic book
Author Adimurthi, editor
Sandeep, K., editor
Schindler, Ian, editor
Tintarev, Kyril, editor
School and Workshop on Cocompact Imbeddings, Profile Decompositions, and Their Applicatons to PDE (2012 : Bangalore, India)
ISBN 3034803737 (electronic bk.)
9783034803731 (electronic bk.)