Partial Differential Equations and the Calculus of Variations: Essays in Honor of Ennio De Giorgi

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 ?t2 +a (t)??2.- 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.- On a class of nonlinear diagonal elliptic systems with critical growth and C?-regularity.- Higher integrahility from reverse Jensen inequalities with different supports.- Partial regularity of cartesian currents which minimize certain variational integrals.- Théorème des minimax locaux et fonctions topologiquement fermées.- Variational principles with linear growth.- Estimation de l'erreur dans des problèmes de Dirichlet où apparaît un terme étrange.- On atypical variational problems.- Sur la contrólahilité exacte élargie.- Low and high frequency vibration in stiff problems.- A time-discretization scheme approximating the non-linear evolution equation ut + ABu = 0.- The stored-energy for some discontinuous deformations in nonlinear elasticity.- The calculus of variations and some semilinear variational inequalities of elliptic and parabolic type.- Some remarks on the dependence domain for weakly hyperbolic equations with constant multiplicity.- Monotonicity of the energy for entire solutions of semilinear elliptic equations.- Pseudo-differential operators of Volterra type on spaces of ultra-distributions and parabolic mixed problems.- The Neumann problem for second order elliptic equations with rapidly oscillating periodic coefficients in a perforated domain.- Discrete exterior measures and their meaning in applications.- An embedding theorem.- Nonlocal effects induced by homogenization.- On regularity and existence of viscosity solutions of nonlinear second order, elliptic equations.- Etude d'un système en multiplicité 4 lorsque le degrée du polinôme minimal est petit.- On the Weierstrass integrals of the calculus of variations over BV varieties: recent results of the mathematical seminar in Perugia.- Variable structures control of semilinear evolution equations.