My research has been supported by the following grants

  • Divergence-measure fields and nonlinear conservation laws, National Science Foundation (Analysis), DMS-0540869, 2005-2009.
  • Purdue Research Foundation, Summer Faculty Award, 2008.
  • Divergence-measure fields and the structure of solutions of systems of hyperbolic conservation laws, National Science Foundation (Analysis), DMS-090245, 2009-2014.
  • PRF International Travel Grant, Summer 2016.
  • Simons Foundation, Award Number 524190, 2017-2022.

Gauss-Green formulas for divergence-measure fields in L^p, with Giovanni Comi, preprint, 2017.

A fully nonlinear free boundary problem, part II: Lipschitz implies C^{1,alpha}, with L. Caffarelli, S. Patrizi and V. Quitalo, in preparation, 2017.

Divergence-measure fields and non-linear conservation laws, with Gui-Qiang Chen, in preparation, 2017.

Characterization of signed measures in the dual of BV and related isometric isomorphisms, with N. C. Phuc, Annali della Scuola Normale Superiore di Pisa, (5), Vol. XVII, 1-33, 2017 . 

One-sided approximation of sets of finite perimeter, with Giovanni Comi, Rend. Lincei Mat. Appl., 28, 181-190, 2017.

Morrey spaces and generalized Cheeger sets, with Qinfeng Li,  Advances in Calculus of Variations, accepted, 2017.

On the dual of BV, Contemporary Mathematics, Accepted,  2016. 

Occupational measures and averaged shape optimization, with Qinfeng Li and Ido Bright, ESAIM: Control, Optimization and Calculus of Variations, 1-25, 2017.

Modern Real Analysis, with W. Ziemer, Graduate Texts in Mathematics, Springer,  398 pp. , 2017.

The integral of the normal and fluxes over sets of finite perimeter, with Ido Bright, Interfaces and free boundaries, 17, 245-259, 2015.

On the distributional divergence of vector fields vanishing at infinity, with Thierry DePauw, Proceedings of the Royal Society of Edinburgh, 141A, 65-76, 2011.

On the structure of solutions of nonlinear hyperbolic systems of conservation laws, with G. Q. Chen, Communications on Pure and Applied Analysis, Volume 10, Number 4, 1011-1036, 2011.

Existence of traveling wave solutions of a high-order nonlinear acoustic wave equation, with M. Chen and T. Walsh, Physics Letters A, Volume 373, Issue 11, 1037-1043, 2009.

Gauss-Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws, with G.Q. Chen and W. Ziemer, Communication on Pure and Applied Mathematics, 62, No 2, 242-304, 2009.

Characterizations of the existence and removable singularities of divergence-measure vector fields, with N.C. Phuc, Indiana University Mathematics Journal, Volume 57, Number 4, 1573-1598, 2008.

Finite element methods for non-linear acoustics and fluids, with Timothy Walsh, Journal of Computational Acoustics, Vol. 15, No. 3, 353-375, 2007.

Measure-theoretic analysis and non-linear conservation laws, with G.Q. Chen and W. Ziemer, Pure and Applied Mathematics Quarterly, 3 (3), 841-879, 2007.

Divergence-measure fields, sets of finite perimeter and conservation laws, with G.Q. Chen, Arch. Rat. Mech. Anal.,175,. no.2 245-267, 2005.

Level set methods to compute minimal surfaces in a medium with exclusions (voids)., with D. Chopp and T. Walsh, Interfaces Free Bound. {\bf 7} (2005), no.~2, 161-185.

Plane-like minimal surfaces in periodic media with exclusions, SIAM J. Math. Anal. 36 (2004), no. 2, 523--551.

Generalized Snell's law for weighted minimal surfaces in heterogeneous media, with L. Zhilin, L. Xiaobiao and H.Zhao, Methods Appl. Anal. 10 (2003), no. 2, 199-214.