Publications
[50] Sharp order of vanishing for parabolic equations, nodal set estimates and Landis type results.
(with V. Arya and N. Garofalo)
[49] An observation on eigenfunctions of the Laplacian.
(with N. Garofalo)
[48] Sharp asymptotic of solutions to some nonlocal parabolic equations.
(with A. Ghosh)
arXiv:2306.00341
[47] Extension problem for the fractional parabolic Lam\'e operator and unique continuation.
(with S. Senapati)
arXiv:2208.11598.
[46] An improved Rellich type estimate for the eigenfunctions of the Baouendi-Grushin operator.
(with N. Garofalo)
arXiv:2311.11559, to appear in Journal d’Analyse Mathematique.
[45] Higher order Boundary Schauder Estimates in Carnot Groups.
(with N. Garofalo and I. Munive)
arXiv:2210.12950, to appear in Math. Ann.
[44] The Calderón problem for space-time fractional parabolic operators with variable coefficients.
(with S. Senapati)
arXiv:2205.12509, to appear in SIAM. J. Math. Anal.
[43] Decay at infinity for solutions to some fractional parabolic equations.
(with A. Ghosh)
arXiv:2307:10887, to appear in Proceedings of the Royal Society of Edinburgh, Section A: Mathematics.
[42] Strong unique continuation for variable coefficient parabolic operators with Hardy type potential.
(with P. Ganguly and A. Ghosh)
J. Differential Equations 380 (2024), 92-145.
[41] On the forward in time propagation of zeros in fractional heat type problems.
(with N. Garofalo)
Arch. Math. (Basel) 121 (2023), no. 2, 189-195.
[40] Quantitative uniqueness for fractional heat type operators.
(with V. Arya)
Calc. Var. Partial Differential Equations 62 (2023), no. 7, Paper No. 195, 47 pp.
[39] Borderline gradient continuity for the normalized $p$-parabolic operator.
(with M. Akman and I. Munive)
J. Geom. Anal. 33 (2023), no. 8, 264.
[38] Space-like quantitative uniqueness for parabolic operators.
(with V. Arya)
J. Math. Pure. Appl. (9) 177 (2023), 214-259.
[37] On the space-like analyticity in the extension problem for some nonlocal parabolic equations.
(with N. Garofalo)
Proc. Amer. Math. Soc. 151 (2023), no. 3, 1235-1246.
[36] Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic p-Laplace equations.
( with P. Garain and J. Kinnunen)
Commun. Contemp. Math. 25 (2023), no. 8, Paper No. 2250032, 23 pp.
[35] Unified approach to C 1,α regularity for quasilinear parabolic equations.
( with K. Adimurthi)
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 33 (2022), no. 4, 833-883.
[34] Space-like strong unique continuation for some fractional parabolic equations.
(with V. Arya, D. Danielli and N. Garofalo)
J. Funct. Anal. 284 (2023), no. 1, Paper No. 109723.
[33] The thin obstacle problem for some variable coefficient degenerate elliptic operators.
(with F. Buseghin and N. Garofalo)
Nonlinear Anal. 223 (2022), 42 pp.
[32] Borderline regularity for fully nonlinear equations in Dini domains.
(with K. Adimurthi)
Adv. Calc. Var. 15 (2022), no. 4, 619-634.
[31] Some local properties of subsolutions and supersolutions for a doubly nonlinear nonlocal parabolic p-Laplace equation.
(with P. Garain and J. Kinnunen)
Ann. Mat. Pura Appl. (4) 201 (2022), no.4, 1717-1751.
[30] Regularity for parabolic systems with critical growth in the gradient and applications.
( with G. D´avila and Y. Sire)
J. Anal. Math. 146 (2022), no. 1, 365-383.
[29] C^{1, \alpha} regularity for degenerate fully nonlinear elliptic with Neumann boundary conditions.
(with R. B. Verma)
Potential Anal. 57 (2022), no.3, 327-365.
[28] Carleman estimates for Baouendi-Grushin operators with applications to quantitative uniqueness and strong unique continuation.
(with N. Garofalo and R. Manna)
Appl. Anal. 101 (2022), no. 10, 3667-3688.
[27] Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation.
(with R. Manna)
Discrete Contin. Dyn. Syst. 41 (2021), no. 11, 5105-5139.
[26] The structure of the singular set in the thin obstacle problem for degenerate parabolic equations.
( with D. Danielli, N. Garofalo and A. Petrosyan)
Calc. Var. Partial Differential Equations 60 (2021), no. 3, Paper No. 91, 52 pp.
[25] Strong Backward uniqueness for sublinear parabolic equations.
(with V. Arya)
NoDEA Nonlinear Differential Equations Appl. 27 (2020), no. 6, Paper No. 50, 18 pp.
[24] On a Bernoulli-type overdetermined free boundary problem.
( with M. Akman and MSV Garcia)
Ann. Fenn. Math. 46 (2021), no. 2, 601-618.
[23] A strong unique continuation property for the heat operator with Hardy type potential.
( with N. Garofalo and R. Manna)
J. Geom. Anal. 31 (2021), no. 6, 5480-5504.
[22] The Harnack inequality for a class of non local parabolic equations.
(with N. Garofalo, I. Munive and D. Nhieu)
Commun. Contemp. Math. 23 (2021), np. 6, Paper No. 2050050, 23pp.
[21] Twice differentiability of solutions to fully nonlinear parabolic equations near the boundary.
(with K. Adimurthi and R.B. Verma)
Nonlinear Anal. 197 (2020), 111830, 16 pp.
[20] Space like strong unique continuation for sublinear parabolic equations.
(with R. Manna)
J. Lond. Math. Soc. (2) 102 (2020), no. 1, 205-228.
[19] The regular free boundary in the thin obstacle problem for degenerate parabolic equations.
(with D. Danielli, N. Garofalo and A. Petrosyan)
Algebra i Analiz 32 (2020), no. 3, 84-126.
[18] Gradient continuity estimates for the normalized pPoisson equation.
(with I. Munive)
Commun. Contemp. Math. 22 (2020), no. 8, 1950069, 24 pp.
[17] On the Strong unique continuation property of a degenerate elliptic operator with Hardy type potential.
(with A. Mallick)
Ann. Mat. Pura Appl. (4) 199 (2020), no. 1, 1-21.
[16] Compactness methods for \Gamma^{1, \alpha} boundary Schauder estimates in Carnot groups.
(with N. Garofalo and I. Munive)
Calc. Var. Partial Differential Equations 58 (2019), no. 3, Art. 97, 29 pp.
[15] Monotonicity of generalized frequencies and strong unique continuation property for fractional parabolic equations.
(with N. Garofalo)
Adv. Math. 336 (2018), 149-241.
[14] Sharp vanishing order of solutions to stationary Schrodinger equations on Carnot groups of arbitrary step.
J. Math. Anal. Appl. 465 (2018), no. 1, 571-587.
[13] Overdetermined problems for the normalized p-Laplacian.
(with B. Kawohl)
Proc. Amer. Math. Soc. Ser. B 5 (2018), 18-24.
[12] Higher regularity of the free boundary in the parabolic Signorini problem.
(with MSV Garcia and A. Zeller)
Calc. Var. Partial Differential Equations 56 (2017), no. 1, 26pp.
[11] Quantitative uniqueness for elliptic equations at the boundary of C1, Dini domains.
(with N. Garofalo)
Journal of Differential Equations, 261 (2016), 6718- 6757.
[10] Quantitative uniqueness for zero-order perturbations of generalized Baouendi-Grushin operators.
(with N. Garofalo)
Rend. Istit. Mat. Univ. Trieste 48 (2016), 189-207. 35H20 (35A30).
[9] A parabolic analogue of higher order comparison theorem of De Silva and Savin.
(with N. Garofalo)
J. Differential Equations 260 (2016), 1801-1829.
[8] Modica type gradient estimates for reaction diffusion equations.
(with N. Garofalo)
Geometric methods in PDE’s, 215-242, Springer INdAM Ser., 13.
[7] Modica Type gradient estimates for an inhomogeneous variant of the normalized p-laplacian evolution.
(with N. Garofalo)
Nonlinear Analysis 121 (2015) 458-468.
[6] A note on the unique continuation property for fully nonlinear elliptic equations.
Commun. Pure Appl. Anal. 14 (2015), no. 2, 623-626.
[5] On the Dirichlet boundary Value problem for the normalized p-Laplacian evolution.
(with N. Garofalo)
Commun. Pure Appl. Anal. 14 (2015), no. 1, 1-21.
[4] Boundary behavior of non-negative solutions of fully nonlinear parabolic equations.
(with N. Garofalo)
Manuscripta Math. 146 (2015), no. 1-2, 201-222.
[3] Gradient bounds for p-harmonic systems with vanishing Neumann (Dirichlet) Data in a convex domain.
(with J. Lewis)
Nonlinear Anal. 100 (2014), 78- 85.
[2] A remark on a vanishing property of viscosity solutions of fully nonlinear parabolic equations.
Nonlinear Anal. 80 (2013), 14-17.
[1] Gradient bounds and Monotonicity of energy for some nonlinear singular diffusion equations.
(with N. Garofalo)
Indiana Univ. Math. J. 62 (2013), 699- 736.