Research Monograph

Functional Inequalities: New Perspectives and Applications, Mathematical Surveys and Monographs, American Mathematical Society, 2013 (with N. Ghoussoub).

Research Papers

  • Symmetry and uniqueness of solutions to some Liouville-type equations and systems, Submitted (with C. Gui, A. Jevinkar), PDF.

  • Electrical Networks with Prescribed Current and Applications to Random Walks on Graphs, Submitted (with C. Knox), PDF.

  • The Sphere Covering Inequality and Its Applications, Inventiones Mathematicae, to appear (with Changfeng Gui), PDF.

  • Uniqueness of solutions of mean field equations in $\R^2$, Proc. Amer. Math. Soc., to appear (with Changfeng Gui), PDF.

  • Symmetry of solutions of a mean field equation on flat tori, International Mathematics Research Notices, to appear (with Changfeng Gui), PDF.

  • Least Gradient Problems with Neumann Boundary Condition, Journal of Differential Equations, to appear PDF.

  • Existence and structure of minimizers of least gradient problems, Indiana University Math Journal, to appear, PDF.

  • Photo-acoustic tomography in a rotating measurement setting, Inverse Problems, to appear (with G. Bal), PDF.

  • Uniqueness of minimizers of weighted least gradient problems arising in conductivity imaging, Calculus of Variations and Partial Differential Equations, to appear (with A. Nachman, A. Tamasan), PDF.

  • Convergence of the alternating split Bregman algorithm in infinite-dimensional Hilbert spaces, preprint (with A. Nachman), PDF.

  • Existence and uniqueness of minimizers of general least gradient problems, (with R.L. Jerrard and A. Nachman), J. Reine Angew. Math., to appear. PDF.

  • Current Density Impedance Imaging with an Anisotropic Conductivity in a Known Conformal Class, SIAM J. Math. Anal., 46 (2014), 3969-3990 (with N. Hoell and A. Nachman), PDF.

  • A convergent algorithm for the hybrid problem of reconstructing conductivity from minimal interior data, Inverse Problems 28 (2012), 084003 (with A. Nachman and A. Timonov) PDF.

  • Conductivity imaging from one interior measurement in the presence of perfectly conducting and insulating inclusions, SIAM J. Math. Anal., 44 (2012), 3969-3990 (with A. Nachman and A. Tamasan) PDF.

  • Radial symmetry of large solutions of semilinear elliptic equations with advection, Proc. Roy. Soc. Edinburgh Sect. A, 144 (2014), 139-147 (with E. Kamalinejad), PDF.

  • Optimal weighted Hardy-Rellich inequalities on H^2 \cap H^1_0, J. London. Math. Soc., 85 (2012), 22-40 PDF.

  • Sharp counterexamples related to De Giorgi conjecture in dimensions 4\leq n \leq 8, Proc. Amer. Math. Soc., 142 (2014), 199-203, PDF.

  • Isolated singularities of polyharmonic inequalities, J. Funct. Anal., 261 (2011) 660-680 (with M. Ghergu, and S. Taliaferro) PDF.

  • Bessel pairs and optimal Hardy and Hardy-Rellich inequalities, Math. Annalen, 349 (2011) 1-57 (with N. Ghoussoub) PDF.

  • The critical dimension for a fourth order elliptical problem with singular nonlinearity, Arch. Ration. Mech. Anal., 198 (2010) 763-787 (with C. Cowan, P. Esposito, and N. Ghoussoub) PDF.

  • The singular extremal solutions of the bilaplacian with exponential nonlinearity, Proc. Amer. Math Soc., 138 (2010), 1287-1293 PDF.

  • On the critical dimension of a fourth order elliptic problem with negative exponent, Journal of Differential Equations, 248 (2010), 594-616 PDF.

  • On the best possible remaining term in the improved Hardy inequality, Proc. Nat. Acad. Sci. U.S.A., 105 (2008), 13746-13751, (with N. Ghoussoub) PDF.

Complete list of publications can be found in my CV.