Partial Differential Equations and the Calculus of Variations

An improvement of Cartan's test for ordinarity.- A mathematical contribution to Gibbs's analysis of fluid phases in equilibrium.- The epi-continuation method for minimization problems. Relation with the degree theory of F.Browder for maximal monotone operators.- Discretization of evolution variational inequalities.- Homogenization for non linear elliptic equations with random highly oscillatory coefficients.- L? and L1 variations on a theme of ? -convergence.- Asymptotics for elliptic equations involving critical growth.- Asymptotic behaviour for Dirichlet problems in domains bounded by thin layers.- Fundamental interior estimates for a class of second order elliptic operators.- ?-Convergence of integral functionals defined on vector-valued functions.- Limits of obstacle problems for the area functional.- Some remarks on the well-posedness of the Cauchy problem in Gevrey spaces.- Approximating measures and rectifiable curves.- A non-uniqueness result for the operators with principal part ?2t + a(t)?2x.- A note on duality and the calculus of variations.- Some results on periodic solutions of Hamilton-Jacobi equations in Hilbert spaces.- Generalized solutions to ordinary differential equations with discontinuous right-hand sides via ?-convergence.- Stationary solutions of nonlinear Schrödinger equations with an external magnetic field.- On the touching principle.- Generalized solutions and convex duality in optimal control.- Models of self-descriptive set theories.