1. CJM Online first
 Phan, Tuoc

Lorentz estimates for weak solutions of quasilinear parabolic equations with singular divergencefree drifts
This paper investigates regularity in Lorentz
spaces of weak solutions of a class of divergence form quasilinear
parabolic equations with singular divergencefree drifts. In
this class of equations, the principal terms are vector field
functions which are measurable in $(x,t)$variable, and nonlinearly
dependent on both unknown solutions and their gradients. Interior,
local boundary, and global regularity estimates in Lorentz spaces
for gradients of weak solutions are established assuming that
the solutions are in BMO space, the John Nirenberg space.
The results are even new when the drifts are identically zero
because they do not require solutions to be bounded as in the
available literature. In the linear setting, the results of
the paper also improve the standard CalderÃ³nZygmund regularity
theory to the critical borderline case. When the principal term
in the equation does not depend on the solution as its variable,
our results recover and sharpen known, available results. The
approach is based on the perturbation technique introduced by
Caffarelli and Peral together with a "doublescaling parameter"
technique, and the maximal function free approach introduced
by Acerbi and Mingione.
Keywords:gradient estimate, quasilinear parabolic equation, divergencefree drift Categories:35B45, 35K57, 35K59, 35K61 

2. CJM 2009 (vol 62 pp. 74)
 Ducrot, Arnaud; Liu, Zhihua; Magal, Pierre

Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in $L^{p}$ Spaces
We present the explicit formulas for the projectors on the generalized
eigenspaces associated with some eigenvalues for linear neutral functional
differential equations (NFDE) in $L^{p}$ spaces by using integrated
semigroup theory. The analysis is based on the main result
established elsewhere by the authors and results by Magal and Ruan
on nondensely defined Cauchy problem.
We formulate the NFDE as a nondensely defined Cauchy problem and obtain
some spectral properties from which we then derive explicit formulas for
the projectors on the generalized eigenspaces associated with some
eigenvalues. Such explicit formulas are important in studying bifurcations
in some semilinear problems.
Keywords:neutral functional differential equations, semilinear problem, integrated semigroup, spectrum, projectors Categories:34K05, 35K57, 47A56, 47H20 

3. CJM 1997 (vol 49 pp. 798)