Publications:
- Singular sets of a class of
locally conformally flat manifolds, Duke Mathematical Journal,
129, no. 3 (2005), 551–572 .pdf
- Removability of singularities
for a class of fully non-linear elliptic equations, Calc.Var.
and PDE, 27 (2006), no. 4, 439–466 .pdf
- Classification of singularities
for a subcritical fully non-linear problem, Pacific J. Math. 226
(2006), no. 1, 83–102 .pdf
- Asymptotics for a symmetric equation in
price formation, joint with M. Gualdani. App. Math. Optim. 59
(2009), 233–246 .pdf
- Gamma convergence of an energy
functional related to the fractional Laplacian, Calc.Var. and
PDE, 36 (2009), no. 2, 173-210 .pdf
- Global existence and uniqueness
of solutions to a model of price formation, joint with L.
Chayes, M. Gualdani and I. Kim. SIAM J. Math. Anal. Volume 41, Issue 5,
pp. 2107-2135 (2009) .pdf
- Fractional Laplacian in
conformal geometry, joint with A. Chang. Advances in
Mathematics,Volume 226, Issue 2, pages 1410-1432, (2011) .pdf
- Asymptotics for a free-boundary
model in price formation, joint with M. Gualdani, Nonlinear
Analysis: Theory, Methods&Applications, 74 (2011), 3269–3294
.pdf
- Slow motion of particle systems
as a limit of a reaction-diffusion equation with fractional Laplacian, joint with R. Monneau.
Discrete and Continuous Dynamical Systems - A, Vol. 32, no. 4 (2012), 1255-1286.
.pdf
- Singular solutions of
fractional order conformal Laplacians, joint with and R. Mazzeo
and Y. Sire, to appear in Journal of Geometric Analysis
.pdf
- Some non-standard Sobolev
spaces: interpolation and its application to PDE, joint with
M. Gualdani, to appear in Acta Applicanda Mathematicae .pdf
Preprints:
- Fractional conformal Laplacians
and fractional Yamabe problems, joint with J. Qing
.pdf
- Classical Solutions for a
nonlinear Fokker-Planck equation arising in Computational Neuroscience,
joint
with J. Carrillo, M. Gualdani and M. Schonbek .pdf
- A weighted notion of
renormalized volume related to the fractional
Laplacian .pdf
- A perturbation argument for a
Monge-Ampere type equation arising in optimal transportation,
joint with L. Caffarelli and T. Nguyen .pdf
In
preparation:
- Constant sigma_k curvature
metrics with non isolated singularities, joint with L. Mazzieri
- A Discrete Bernoulli free
boundary Problem, joint with M. Gualdani and H. Shahgholian
- ... joint with M. Saez