Concentration Analysis and Applications to PDE: ICTS Workshop, Bangalore, January 2012

Description

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. This 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 Front Matter....Pages i-x On the Elements Involved in the Lack of Compactness in Critical Sobolev Embedding....Pages 1-15 A Class of Second-order Dilation Invariant Inequalities....Pages 17-28 Blow-up Solutions for Linear Perturbations of the Yamabe Equation....Pages 29-47 Extremals for Sobolev and Exponential Inequalities in Hyperbolic Space....Pages 49-67 The Ljapunov–Schmidt Reduction for Some Critical Problems....Pages 69-83 A General Theorem for the Construction of Blowing-up Solutions to Some Elliptic Nonlinear Equations via Lyapunov– Schmidt’s Finite-dimensional Reduction....Pages 85-116 Concentration Analysis and Cocompactness....Pages 117-141 A Note on Non-radial Sign-changing Solutions for the Schrödinger–Poisson Problem in the Semiclassical Limit....Pages 143-156