Perspectives in Nonlinear Partial Differential Equations

Vortex patterns in Bose Einstein condensates by A. Aftalion Concentration phenomena for nonlinear Schrodinger equations: Recent results and new perspectives by A. Ambrosetti and A. Malchiodi On the chain rule for the divergence of $BV$-like vector fields: Applications, partial results, open problems by L. Ambrosio, C. De Lellis, and J. Maly Compactness by A. Bahri Generalized travelling waves for reaction-diffusion equations by H. Berestycki and F. Hamel Some questions related to the lifting problem in Sobolev spaces by F. Bethuel and D. Chiron Normal forms and the nonlinear Schrodinger equation by J. Bourgain Extremal solutions and instantaneous complete blow-up for elliptic and parabolic problems by X. Cabre Capillary drops on an inhomogeneous surface by L. A. Caffarelli and A. Mellet Diffusive Lagrangian transformations, Navier-Stokes equations and applications by P. Constantin Some open problems on the control of nonlinear partial differential equations by J.-M. Coron The 1-Laplacian, the $\infty$-Laplacian and differential games by L. C. Evans Probabilistic approach to a class of semilinear partial differential equations by J.-F. Le Gall Variational methods in image processing by A. Haddad and Y. Meyer Null hypersurfaces with finite curvature flux and a breakdown criterion in general relativity by S. Klainerman Some Liouville theorems and applications by Y. Li Analysis on Faddeev knots and Skyrme solitons: Recent progress and open problems by F. Lin and Y. Yang The precise boundary trace of positive solutions of the equation $\Delta u=u^q$ in the supercritical case by M. Marcus and L. Veron Blow-up in nonlinear heat equations with supercritical power nonlinearity by H. Matano Sobolev maps on manifolds: Degree, approximation, lifting by P. Mironescu Partial and full symmetry of solutions of quasilinear elliptic equations, via the comparison principle by P. Pucci, B. Sciunzi, and J. Serrin Single and multi-transition solutions of a family of pde's by P. H. Rabinowitz Some methods and issues in the dynamics of vortices in the parabolic Ginzburg-Landau equations by S. Serfaty.