One-Layer Free Boundary Problems with Two Free Boundaries -- New Numerical Solutions for the Brezis-Nirenberg Problem on $$\mathbb{S}^n $$ -- On some Boundary Value Problems for Incompressible Viscous Flows with Shear Dependent Viscosity -- Radiative Heat Transfer in Silicon Purification -- A Decay Result for a Quasilinear Parabolic System -- The Shape of Charged Drops: Symmetrybreaking Bifurcations and Numerical Results -- On the One-dimensional Parabolic Obstacle Problem with Variable Coefficients -- Hardy Potentials and Quasi-linear Elliptic Problems Having Natural Growth Terms -- Recent Advances on Similarity Solutions Arising During Free Convection -- Rellich Relations for Mixed Boundary Elliptic Problems -- Lyapunov-type Inequalities and Applications to PDE -- Gaeta 2004. Elliptic Resonant Problems with a Periodic Nonlinearity -- Harnack Inequality for p-Laplacians on Metric Fractals -- Wave Propagation in Discrete Media -- A Solution of the Heat Equation with a Continuum of Decay Rates -- Finite Volume Scheme for Semiconductor Energy-transport Model -- Asymptotic Behavior of Nonlinear Parabolic Problems with Periodic Data -- Geodesic Computations for Fast and Accurate Surface Remeshing and Parameterization -- On the Newton Body Type Problems -- Some Open Problems on Water Tank Control Systems -- Hölder Estimates for Solutions to a Singular Nonlinear Neumann Problem -- Asymptotic Analysis of the Neumann Problem for the Ukawa Equation in a Thick Multi-structure of Type 3:2:2 -- On the Haïm Brezis Pioneering Contributions on the Location of Free Boundaries -- Fractal Conservation Laws: Global Smooth Solutions and Vanishing Regularization -- Stationary and Self-similar Solutions for Coagulation and Fragmentation Equations -- Orlicz Capacities and Applications to PDEs and Sobolev Mappings -- Energy Forms on Non Self-similar Fractals -- Measure Data and Numerical Schemes for Elliptic Problems -- Brezis-Nirenberg Problem and Coron Problem for Polyharmonic Operators -- Local and Global Properties of Solutions of a Nonlinear Boundary Layer Equation -- Mathematical Models of Aggregation: The Role of Explicit Solutions -- Metastable Behavior of Premixed Gas Flames -- Recent Progress on Boundary Blow-up -- Maximum Principle for Bounded Solutions of the Telegraph Equation: The Case of High Dimensions -- Kolmogorov Equations in Physics and in Finance -- Harnack Inequalities and Gaussian Estimates for a Class of Hypoelliptic Operators -- How to Construct Good Measures -- Bifurcation and Asymptotics for Elliptic Problems with Singular Nonlinearity -- A Model for Hysteresis in Mechanics Using Local Minimizers of Young Measures -- The Precise Lp-theory of Elliptic Equations in the Plane -- Essential Spectrum and Noncontrollability of Membrane Shells -- The Porous Medium Equation. New Contractivity Results -- Large Solutions of Elliptic Equations with Strong Absorption -- Relaxation in Presence of Pointwise Gradient Constraints.