Proceedings of the 4th European Conference, elliptic and parabolic problems : Rolduc and Gaeta 2001 : Rolduc, Netherlands, 18-22 June 2001, Gaeta, Italy, 24-28 September 2001

This book provides an overview of the state of the art in important subjects, including ? besides elliptic and parabolic issues ? geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis. CONTENTS Preface 1. Rolduc Models for shape memory alloys described by subdifferentials of indicator functions Semilinear elliptic boundary value problems with critical Sobolev exponent Diffraction problems for quasilinear elliptic and parabolic systems Extremality and compactness results for elliptic hemivariational inequalities On an operator equation for Stokes boundary value problems Local stability under changes of boundary conditions at a far away location On some variational problems with an infinite number of wells Boltzmann Equation for Quantum Particles and Fokker Planck approximation Boundedness of global solutions of nonlinear parabolic equations Transmission problems for degenerate parabolic equations Existence of solutions of a segregation model arising in population dynamics The nonstationary Stokes and Navier-Stokes equations in aperture domains Global attractors for multivalued flows associated with subdifferentials Quasiconvex extreme points of convex sets The Richards equation for the modeling of a nuclear waste repository Trace identities and universal estimates for eigenvalues of linear pencils Universal estimates for the blow-up rate in a semilinear heat equation Asymptotic behavior of curves evolving by forced curvature flows Existence of non-steady flows of an incompressible, viscous drop of fluid in a frame rotating with finite angular velocity On a convection-diffusion equation with partial diffusivity Quasiconvexity and optimal design A regularity criterion for the angular velocity component in the case of axi-symmetric Navier-Stokes equations A comparison principle for the p-Laplacian Supercritical variational problems with unique critical points Structure of the solution flow for steady-state problems of one-dimensional Frémond models of shape memory alloys Lagrangian coordinates in free boundary problems for multidimensional parabolic equations The Brézis-Nirenberg problem on H^n Existence and uniqueness of solutions Solvability of general elliptic problems in Hölder spaces 2. Gaeta Nonlinear diffusion in irregular domains Analysis of radiative transfer equation coupled with nonlinear heat conduction equation Viscosity Lyapunov functions for almost sure stability of degenerate diffusions Mass transport through charged membranes The Hopf solution of Hamilton-Jacobi equations Conservation of critical groups in a weaker topology for functionals associated with quasilinear elliptic equations Approximating exterior flows by flows on truncated exterior domains: piecewise polygonal artificial boundaries On the Stefan problem with surface tension Epidemic models with compartmental diffusion Algebraic multigrid for selected PDE systems Numerical computation of electromagnetic guided waves in a general perturbed stratified medium A non-stationary model for catalytic converters with cylindrical geometry Exact controllability of piezoelectric shells Optimal control approach for the fluid-structure interaction problems Hyperbolic propagation of singularities in a parabolic system of shell theory Singular perturbations going out of the energy space. Layers in elliptic and parabolic cases Regularity and uniqueness results for a phase change problem in binary alloys Bifurcation in population dynamics An overview of the state of the art in important subjects, including - besides elliptic and parabolic issues - geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modelling and numerical analysis.