Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
H. Abels
Bounded Imaginary Powers and H∞-Calculus of
the Stokes Operator in Unbounded Domains . . . . . . . . . . . . . . . . . . . . . . . . 1
M. Borsuk and A. Zawadzka
Exact Estimates of Solutions to the Robin Boundary Value Problem
for Elliptic Non-divergent Second-order Equations in a Neighborhood
of the Boundary Conical Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
D. Bothe, J. Pr¨uss and G. Simonett
Well-posedness of a Two-phase Flow with Soluble Surfactant . . . . . . . . 37
J. Brasche and M. Demuth
Resolvent Differences for General Obstacles . . . . . . . . . . . . . . . . . . . . . . . . . 63
J.I. D´ıaz
Special Finite Time Extinction in Nonlinear Evolution
Systems: Dynamic Boundary Conditions and
Coulomb Friction Type Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
M. Duelli and L. Weis
Spectral Projections, Riesz Transforms and
H∞-calculus for Bisectorial Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
R. Farwig, G.P. Galdi and H. Sohr
Very Weak Solutions of Stationary and Instationary
Navier-Stokes Equations with Nonhomogeneous Data . . . . . . . . . . . . . . . 113
M. Fila, J.J.L. Vel´azquez and M. Winkler
Grow-up on the Boundary for a Semilinear Parabolic Problem . . . . . . 137
H. Gajewski and I.V. Skrypnik
Existence and Uniqueness Results for Reaction-diffusion Processes
of Electrically Charged Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
F. Colombo and D. Guidetti
An Inverse Problem for a Phase-field Model in Sobolev Spaces . . . . . . 189
vi Contents
O. Anza Hafsa and M. Chipot
Numerical Analysis of Microstructures:
The Influence of Incompatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
J. Hern´andez, F.J. Mancebo and J.M. Vega
Nonlinear Singular Elliptic Problems:
Recent Results and Open Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
M. Hieber
The Navier-Stokes Flow in the Exterior of Rotating Obstacles . . . . . . . 243
M. Kuˇcera, J. Eisner and L. Recke
A Global Bifurcation Result for Variational Inequalities . . . . . . . . . . . . . 253
P.C. Kunstmann
On Elliptic Non-divergence Operators with
Measurable Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
P. Lauren¸cot and D. Wrzosek
A Chemotaxis Model with Threshold Density and
Degenerate Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
J. L´opez-G´omez and M. Molina-Meyer
In the Blink of an Eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
J. L´opez-G´omez and C. Mora-Corral
Generalized Minimal Cardinal of the λ-slices of the Semi-bounded
Components Arising in Global Bifurcation Theory . . . . . . . . . . . . . . . . . . 329
S.A. Messaoudi
Blow-up of Solutions of a Semilinear Heat Equation with
a Visco-elastic Term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
C.M. Murea and G. Hentschel
Finite Element Methods for Investigating the Moving
Boundary Problem in Biological Development . . . . . . . . . . . . . . . . . . . . . . . 357
J. Naumann
Existence of Weak Solutions to the Equations of Stationary
Motion of Heat-conducting Incompressible Viscous Fluids . . . . . . . . . . . 373
P. Pol´aˇcik and P. Quittner
Liouville Type Theorems and Complete Blow-up for
Indefinite Superlinear Parabolic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 391
D. Praˇz´ak
On Reducing the 2d Navier-Stokes Equations to
a System of Delayed ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
J. Rehberg
Quasilinear Parabolic Equations in Lp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
Contents vii
A. Rodr´ıguez-Bernal
Parabolic Equations in Locally Uniform Spaces . . . . . . . . . . . . . . . . . . . . . 421
B. Scarpellini
Bifurcation of Traveling Waves Related to the B´enard Equations
with an Exterior Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
H.-J. Schmeißer and W. Sickel
Vector-valued Sobolev Spaces and
Gagliardo-Nirenberg Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463
P. Souplet
The Influence of Gradient Perturbations on Blow-up Asymptotics in
Semilinear Parabolic Problems: A Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
Kenichiro Umezu
Non-existence of Positive Solutions for Diffusive Logistic Equations
with Nonlinear Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
A. Rodr´ıguez-Bernal and A. Vidal-L´opez
Extremal Equilibria and Asymptotic Behavior of
Parabolic Nonlinear Reaction-diffusion Equations . . . . . . . . . . . . . . . . . . . 509
C. Walker
A Remark on Continuous Coagulation-Fragmentation Equations
with Unbounded Diffusion Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
P. Weidemaier
On Lp-Estimates of Optimal Type for the Parabolic Oblique
Derivative Problem with VMO-Coefficients – A Refined Version . . . . . 529
