PREPRINTS
This page contains links to copies of some of my most recent papers in
pdf format. The page will be supplemented by an archival page eventually, with
all
of my old papers. This page only contains links to more recent papers.
This research is supported by the division of Mathematical Sciences in the National Science Foundation. I thank the NSF for providing this essential support.
Central Limit Theorem for Maxwellian
Molecules and
Truncation
of the Wild Expansion, with M.C. Carvalho and E. Gabetta. Published
in Comm Pure and Appl. Math., Vol. LIII (2000), pp. 370-397.
Many-Body Aspects of Approach to Equilibrium
with
M.C. Carvalho and Michael Loss, in Journes Equations aux derivees partielles, Nantes, 5-9 juin 2000.
Algebraic rate of decrease of excess free
energy
and
the stability of fronts for a non-local phase kinetics equation, I
with M.C. Carvalho and E. Orlandi. Published in Jour. Stat Phys., Vol.
95 (1999) 1069-1117.
Algebraic rate of decrease of excess free
energy
and
the stability of fronts for a non-local phase kinetics equation, II
with M.C. Carvalho and E. Orlandi. Published in Comm. PDE, Vol. 25
(2000) pp. 847-886.
Cases of equality in Bobkov's inequality and
Gaussian
rearrangemint with Clayton Kerce. Published in Calculus of
Variations, Vol. 13 (2001), pp. 1-18
On the optimal choice of coefficients in a
truncated
Wild sum and approximate solutions for the Kac equation, with F.
Salvarani. Published in
Jour. Stat. Phys., vol. 109 no. 1/2,
(2002) pp. 152-277
Determination of the sepctral gap in
Kac's
master
equation and related stochastic evolutions, with M.C. Carvalho and
Michael Loss. Published in Acta Mathematica Vol. 191 (2003) pp. 1-54
Constrained Steepest Descent in the
2-Wasserstein
Metric, with W. Gangbo. Published in Annals of Mathematics, Vol.
157, no. 3, (2003) pp. 1-40
On the solution of a model Boltzmann equation
via
constrained
steepest descent in the 2--Wasserstein metric, with W. Gangbo. Archive for Rational Mechanics and Analysis, 172 no. 1, (2004) 21--64
Fast and slow convergence to equilibrium
Maxwellian
molecules via Wild sums, with X. Lu. Published in Jour. Stat.
Phys., Vol. 112 no. 1/2, (2003) pp. 59-134
Free energy minimizers for a two-species
model
with segregation and liquid-vapour transition with Carvalho, M. C.;
Esposito, R.; Lebowitz, J. L. and Marra, R. Published in Nonlinearity
Vol. 16 (2003), no. 3, 1075--1105.
A sharp analog of Young's inequality on SN,
and related entropy inequalities
with E. Lieb and M. Loss. Journal of Geometric Analysis, 14 (2004), 487-520
On the relation between the rates of
realxation
and convergence of Wild sums for solutions of the Kac equation,
with M.C. Carvalho and E. Gabetta, Jour. Func. Analysis, 220 , no. 2, (2005) 362–387
Phase transitions in equilibrium systems:
microscopic models and mesoscopic free energies
with M. Carvalho, L.Esposito, J. Lebowitz and R. Marrra. Jour. Molecular Phys., 103 No 21--23 (2005) 3141--3151
An entropy dissipation-entropy estimate for
a thin film type equation
with S. Ulusoy. Comm. in Math. Sciences 3, no. 2 (2005) 171-178
Approximate Solutions of the Cahn-Hilliard Equation via Corrections to the Mullins-Sekerka Motion, with Carvalho and Orlandi, Archive for Rational Mech. Analysis, 171 no 1, (2005) 1--55
Some matrix rearrangement inequalities,
with
E. Lieb. Annali di Matematica Pura e Appl., 185, Supplemnnt 5, (2006) 315--324
An inequality of
Hadamard type for permanents
with E. Lieb and M. Loss. Methods and Applications of Analysis, 13, No. 1 (2006) 1--18
Dropplet
minimizers for the Cahn-Hilliard free
energy functional,
with M. Carvalho, L.Esposito, J. Lebowitz and R. Marrra. Jour . Geom. Analysis, 16, No 2 (2006) 233--263
Probabilistic Investigation of the explosion of solutions of the Kac equation with infinite energy initial distribution,
with Gabbetta and Regazzini, Submitted to
Annals of Probability, currently E.S.I. preprint number 1871
On the rate of explosion for infinite energy solutions of the spatially homogeneous Boltzmann equation, with
Gabbetta and Regazzini, Submitted to Journal of
Statistical Physics, currently E.S.I. preprint number 1877
Asymptotic equipartition and long time behavior of solutions of a thin--film equation, with S. Ulusoy, Submitted to Jour. diff. Equations