Department of Mathematics
302 Buchtel Common
Akron, OH 44325-4002
Office: CAS 277
Phone: (330) 972-2569
Fax: (330) 374-8630
- Partial Differential Equations
- Calculus of Variations, Monge-Kantorovich Mass Transportation
- Fluid Dynamics
Publications and Preprints
On the existence, uniqueness and stability of entropy solutions to scalar conservation laws
(with D. Golovaty), 31 pages, submitted.
Interior second derivative estimates for solutions to the linearized
(with C. Gutierrez), 33 pages, submitted.
Interior gradient estimates for solutions to the linearized
(with C. Gutierrez), Advances in Mathematics, vol. 228, 2034--2070, 2011.
On the Cauchy problem for the pressureless Euler-Poisson system
, preprint, April 2011.
Hamilton-Jacobi equations in space of measures associated with a
system of conservation laws
(with J. Feng), to appear in Journal de Mathematiques Pures et Appliquees, 76 pages.
A perturbation argument for a Monge-Ampère type equation arising in optimal transportations
(with L. Caffarelli and M.d.M. González), 55 pages, submitted.
Hamilton-Jacobi equations in the Wasserstein space
(with W. Gangbo and A. Tudorascu), Methods and Applications of Analysis, vol. 15, no. 2, 155--183, 2008.
Euler/Euler-Poisson systems via adhesion dynamics and scalar
(with A. Tudorascu), SIAM J. Math. Analysis, vol. 40, no. 2, 754--775, 2008.
systems as action-minimizing paths in the Wasserstein space
(with W. Gangbo and A. Tudorascu), Arch. Rat. Mech. Analysis, vol. 192, no. 3, 419--452, 2009.
inequalities for bounded domains and singular elliptic equations.
(with D. M. Duc and N. C. Phuc) Indiana University Mathematics Journal, vol. 56,
no. 2, 615--642, 2007.
On Monge-Ampère type equations arising in optimal transportation
(with C. E. Gutierrez) Calc. Var. Partial Differential Equations, vol. 28, no. 3,
Homogenization and convergence of correctors in Carnot groups.
(with B. Franchi and C. E. Gutierrez) Comm. Partial Differential Equations,
vol. 30, no. 10-12, 1817--1841, 2005.
Courses: Fall 2011