Concentration Analysis and Applications to PDE

1. Front Matter

   Pages i-x

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2. On the Elements Involved in the Lack of Compactness in Critical Sobolev Embedding

   • Hajer Bahouri

   Pages 1-15

3. A Class of Second-order Dilation Invariant Inequalities

   • Paolo Caldiroli, Roberta Musina

   Pages 17-28

4. Blow-up Solutions for Linear Perturbations of the Yamabe Equation

   • Pierpaolo Esposito, Angela Pistoia, Jérôme Vétois

   Pages 29-47

5. Extremals for Sobolev and Exponential Inequalities in Hyperbolic Space

   • Gianni Mancini, Kunnath Sandeep

   Pages 49-67

6. The Ljapunov–Schmidt Reduction for Some Critical Problems

   • Angela Pistoia

   Pages 69-83

7. A General Theorem for the Construction of Blowing-up Solutions to Some Elliptic Nonlinear Equations via Lyapunov– Schmidt’s Finite-dimensional Reduction

   • Frédéric Robert, Jérôme Vétois

   Pages 85-116

8. Concentration Analysis and Cocompactness

   • Cyril Tintarev

   Pages 117-141

9. A Note on Non-radial Sign-changing Solutions for the Schrödinger–Poisson Problem in the Semiclassical Limit

   • Giusi Vaira

   Pages 143-156

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.

• partial differential equations

• Centre for Applicable Mathematics Post Bag No. 6503, GKVK Post Office, Tata Institute of Fundamental Research, Bangalore, India

  Adimurthi, K. Sandeep

• CeReMath, Université Toulouse I, Toulouse, France

  Ian Schindler

• Department of Mathematics, Uppsala University, Uppsala, Sweden

  Cyril Tintarev

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