Contents Preface vii On Hai'm Brezis ix Speech of Ha'im Brezis xvii Speech of Michal Govrin xxi Vortex patterns in Bose Einstein condensates AMANDINE AFTALION 1 Concentration phenomena for Nonlinear Schrodinger Equations: recent results and new perspectives ANTONIO AMBROSETTI and ANDREA MALCHIODI 19 On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems LUIGI AMBROSIO, CAMILLO DELELLIS, and JAN MALY 31 Compactness ABBAS BAHRI 69 Generalized travelling waves for reaction-diffusion equations HENRI BERESTYCKI and FRAN_ :OIS HAMEL 101 Some questions related to the lifting problem in Sobolev spaces FABRICE BETHUEL and DAVID CHIRON 125 Normal forms and the nonlinear Schrodinger equation J. BOURGAIN 153 Extremal solutions and instantaneous complete blow-up for elliptic and parabolic problems XAVIER CABRE 159 Capillary drops on an inhomogeneous surface L.A. CAFFARELLI and A. MELLET 175 Diffusive Lagrangian transformations, Navier-Stokes equations and applications PETER CONSTANTIN 203 Some open problems on the control of nonlinear partial differential equations JEAN-MICHEL CORON 215 The 1-Laplacian, the oo-Laplacian and differential games LAURENCE C. EVANS 245 v
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