Publications and Preprints

• (with J.A. Carrillo, M. Di Francesco , A. Figalli , and T. Laurent ) Confinement in nonlocal interaction equations, submitted, preprint
• (with W. Wang, J. Ozolek, A. Lee , C. Chen, G.K. Rohde ) An optimal transportation approach for nuclear structure-based pathology, to appear in IEEE Trans. Med. Imaging. .
• (with J.A. Carrillo, M. Di Francesco , A. Figalli , and T. Laurent ) Global-in-time weak measure solutions, finite-time aggregation and confinement for nonlocal interaction equations, to appear in Duke Math. J., preprint
• (with A. Bertozzi ) Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion, Commun. Pure Appl. Anal. 9 No. 6 (2010) pp.~ 1617-1637. , preprint
• (with S. Lisini , J. A. Carrillo , and G. Savare ) Nonlinear mobility continuity equations and generalized displacement convexity, J. Funct. Anal. 258 (2010) pp. 1273-1309 , preprint, published
• (with J.A. Carrillo) Example of a displacement convex functional of first order, Calc. Var. and PDE 36 (2009) pp. 547-564. preprint, published
• (with S. Esedoglu) Refined upper bounds on the coarsening rate of discrete, ill-posed diffusion equations, Nonlinearity 21 (2008) pp. 2759-2776. preprint, published
• Coarsening in nonlocal interfacial systems, SIAM J. Math. Anal. 40, No. 3, (2008) pp. 1029-1048. preprint, published
• (with K. Glasner, F. Otto, and T. Rump) Ostwald ripening of droplets: The role of migration, European Journal of Applied Mathematics 20, No 1, (2009) pp. 1-67. preprint, published
• (with R. McCann) Second-order asymptotics for the fast-diffusion equation, Internat. Math. Res. Notices (2006), Art. ID 24947, pp. 1-22. preprint, published
• (with F. Otto and T. Rump) Coarsening rates in a droplet model: rigorous upper bounds, SIAM J. Math. Anal. 38, No. 2, (2006), pp. 503-529. preprint, published
• Linear stability of selfsimilar solutions of unstable thin-film equations, Interfaces and Free Boundaries, (2009) no. 3 pp. 375-398. preprint, published
• (with M.C. Pugh) Selfsimilar blowup of unstable thin-film equations, Indiana Univ. Math. J.  54 (2005) no. 6 pp. 1697-1738. preprint, published
• (with F. da Lio and C.I. Kim) Nonlocal front propagation problems in bounded domains with Neumann-type boundary conditions and applications, Asymptotic Analysis 37 (2004) no. 3-4 pp. 257-292. preprint, published
• On level-set approach to motion of manifolds of arbitrary codimension, Interfaces and Free Boundaries, 5 (2003) pp. 417-458. published
• Aproximation schemes for propagation of fronts with nonlocal velocities and Neumann boundary conditions, Nonlinear Analysis, 52 (2003) pp. 79-115. published