Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Andrew Acker
One-Layer Free Boundary Problems with Two Free Boundaries . . . . . . 1
Catherine Bandle and Simon Stingelin
New Numerical Solutions for the Brezis-Nirenberg
Problem on Sn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
H. Beir˜ao da Veiga
On some Boundary Value Problems for Incompressible
Viscous Flows with Shear Dependent Viscosity . . . . . . . . . . . . . . . . . . . . . . 23
A. Berm´udez, R. Leira, M.C. Mu˜niz and F. Pena
Radiative Heat Transfer in Silicon Purification . . . . . . . . . . . . . . . . . . . . . . 33
Said Berrimi and Salim A. Messaoudi
A Decay Result for a Quasilinear Parabolic System . . . . . . . . . . . . . . . . . 43
S.I. Betel´u, M.A. Fontelos and U. Kindel´an
The Shape of Charged Drops: Symmetry-breaking
Bifurcations and Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
A. Blanchet, J. Dolbeault and R. Monneau
On the One-dimensional Parabolic Obstacle Problem
with Variable Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Lucio Boccardo
Hardy Potentials and Quasi-linear Elliptic Problems
Having Natural Growth Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Bernard Brighi and Jean-David Hoernel
Recent Advances on Similarity Solutions
Arising During Free Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
R. Brossard, J.-P. Loh´eac and M. Moussaoui
Rellich Relations for Mixed Boundary Elliptic Problems . . . . . . . . . . . . . 93
A. Ca˜nada, J.A. Montero and S. Villegas
Lyapunov-type Inequalities and Applications to PDE . . . . . . . . . . . . . . . 103
vi Contents
A. Ca˜nada and D. Ruiz
Gaeta 2004. Elliptic Resonant Problems
with a Periodic Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Raffaela Capitanelli
Harnack Inequality for p-Laplacians on Metric Fractals . . . . . . . . . . . . . . 119
Ana Carpio
Wave Propagation in Discrete Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Thierry Cazenave, Fl´avio Dickstein and Fred B. Weissler
A Solution of the Heat Equation with
a Continuum of Decay Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Claire Chainais-Hillairet and Yue-Jun Peng
Finite Volume Scheme for Semiconductor
Energy-transport Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Michel Chipot and Yitian Xie
Asymptotic Behavior of Nonlinear Parabolic Problems
with Periodic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Gabriel Peyr´e and Laurent Cohen
Geodesic Computations for Fast and Accurate
Surface Remeshing and Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
M. Comte
On the Newton Body Type Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Jean-Michel Coron
Some Open Problems on Water Tank Control Systems . . . . . . . . . . . . . . 179
Juan D´avila and Marcelo Montenegro
H¨older Estimates for Solutions to a Singular
Nonlinear Neumann Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
U. De Maio and T.A. Mel’nyk
Asymptotic Analysis of the Neumann Problem for the
Ukawa Equation in a Thick Multi-structure of Type 3 : 2 : 2 . . . . . . . . . 207
J.I. D´ıaz
On the Ha¨ım Brezis Pioneering Contributions on the Location
of Free Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
J´erˆome Droniou
Fractal Conservation Laws: Global Smooth Solutions and
Vanishing Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
M. Escobedo
Stationary and Self-similar Solutions for Coagulation
and Fragmentation Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Contents vii
Alberto Fiorenza
Orlicz Capacities and Applications to PDEs
and Sobolev Mappings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Uta Renata Freiberg and Maria Rosaria Lancia
Energy Forms on Non Self-similar Fractals . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Thierry Gallou¨et
Measure Data and Numerical Schemes for Elliptic Problems . . . . . . . . . 279
Yuxin Ge
Brezis-Nirenberg Problem and Coron Problem
for Polyharmonic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Mohammed Guedda
Local and Global Properties of Solutions
of a Nonlinear Boundary Layer Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
M.A. Herrero
Mathematical Models of Aggregation:
The Role of Explicit Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
S. Kamin, H. Berestycki, L. Kagan and G. Sivashinsky
Metastable Behavior of Premixed Gas Flames . . . . . . . . . . . . . . . . . . . . . . . 319
Satyanad Kichenassamy
Recent Progress on Boundary Blow-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
Jean Mawhin
Maximum Principle for Bounded Solutions of the
Telegraph Equation: The Case of High Dimensions . . . . . . . . . . . . . . . . . . 343
Andrea Pascucci
Kolmogorov Equations in Physics and in Finance . . . . . . . . . . . . . . . . . . . 353
Sergio Polidoro
Harnack Inequalities and Gaussian Estimates for
a Class of Hypoelliptic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
Augusto C. Ponce
How to Construct Good Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
Vicent¸iu R˘adulescu
Bifurcation and Asymptotics for Elliptic Problems
with Singular Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
Marc Oliver Rieger
A Model for Hysteresis in Mechanics Using Local Minimizers
of Young Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
Carlo Sbordone
The Precise Lp-theory of Elliptic Equations in the Plane . . . . . . . . . . . . 415
viii Contents
V. Valente
Essential Spectrum and Noncontrollability of Membrane Shells . . . . . . 423
J.L. V´azquez
The Porous Medium Equation. New Contractivity Results . . . . . . . . . . 433
Laurent V´eron
Large Solutions of Elliptic Equations with Strong Absorption . . . . . . . 453
Elvira Zappale
Relaxation in Presence of Pointwise Gradient Constraints . . . . . . . . . . . 465