Published Papers / Accepted
18. Sharp stability for LSI
Mathematics, (2023) 11, 2670; article.
17. Deficit estimates for the logarithmic Sobolev inequality (with D. Kim)
Differential and Integral Equations, Volume 34, Numbers 7-8 (2021), 437-466; article; arXiv.
16. A weighted relative isoperimetric inequality in convex cones
Methods Appl. Anal. 28 (2021), Number 1; article; arXiv.
15. Boundary regularity and non-transversal intersection for the fully nonlinear obstacle problem
Comm. Pure Appl. Math. 72 (2019), 1459-1473; article; arXiv.
14. Non-transversal intersection of the free and fixed boundary in the mean-field theory of superconductivity
Interfaces and Free Boundaries, 21 (2019), 267-272; article; arXiv.
13. Some remarks on the stability of the Log-Sobolev inequality for the Gaussian measure (with F. Feo, M. Posteraro, and C. Roberto)
Potential Anal. 47 (2017), no.1, 37-52; article.
12. Regularity of solutions in semilinear elliptic theory (with L. Nurbekyan and A. Minne)
Bull. Math. Sci. 7 (2017), Issue 1, 177-200; article; arXiv.
11. A sharp lower bound on the polygonal isoperimetric deficit
Proc. Amer. Math. Soc., 122 (2016), 3115-3122; article; arXiv.
10. Non-transversal intersection of free and fixed boundary for fully nonlinear elliptic operators in two dimensions (with A. Minne) Anal. PDE, Vol. 9 (2016), No. 2, 487-502; article; arXiv.
9. Quantitative logarithmic Sobolev inequalities and stability estimates (with M. Fathi and M. Ledoux)
Discrete Contin. Dyn. Syst., Vol. 36, No. 12, 2016; article; arXiv.
8. Regularity of shadows and the geometry of the singular set associated to a Monge-Ampere equation (with L. Nurbekyan)
Comm. Anal. Geom., Vol. 24, (2016), No. 4, 793-820; article; arXiv.
7. Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems (with A. Minne)
Ann. Inst. H. Poincaré Anal. Non Linéaire, Vol. 33 (2016), No. 5, 1259-1277; article; arXiv.
6. On the stability of the polygonal isoperimetric inequality (with L. Nurbekyan)
Adv. Math., 276 (2015), 62-86; article; arXiv.
5. On the regularity of the free boundary in the optimal partial transport problem for general cost functions (with S. Chen)
J. Differential Equations, 258 (2015), no. 7, 2618-2632; article; arXiv.
4. Obstructions to regularity in the classical Monge problem (with M. Colombo)
Math. Res. Lett., 21, no. 4, 2014; article; arXiv.
3. A quantitative log-Sobolev inequality for a two parameter family of functions (with D. Marcon)
Int. Math. Res. Not. IMRN, (2014) 2014 (20): 5563-5580; article; arXiv.
2. Free boundary regularity in the optimal partial transport problem
J. Funct. Anal., 264 (2013), no. 11, 2497-2528; article; arXiv.
1. A sharp stability result for the relative isoperimetric inequality inside convex cones (with A. Figalli)
J. Geom. Anal., 23 (2013), no. 2, 938-969; article; arXiv.
Conference Proceedings
Free boundary regularity near the fixed boundary for the fully nonlinear obstacle problem
Advances in harmonic analysis and partial differential equations, 147-156, Contemp. Math., 748, Amer. Math. Soc., Providence, RI, 2020; book; arXiv.
Submitted Papers
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1.On the equilibrium shape of a crystal
2. On the first eigenvalue of the Laplacian for polygons
3. Minimizing the free energy (with A. Karakhanyan)
4. The geometry of the free boundary