Publications
Publications
[52] Absence of $L^p$ spectrum for asymptotically flat diffusions in region with cavities.
(with N. Garofalo)
[51] On unique continuation in measure for fractional heat equations.
(with N. Garofalo)
[50] Sharp order of vanishing for parabolic equations, nodal set estimates and Landis type results.
(with V. Arya and N. Garofalo)
Arch. Ration. Mech. Anal. 249 (2025), no. 6, Paper No. 67
[49] An observation on eigenfunctions of the Laplacian.
(with N. Garofalo)
Matematica 3 (2024), no. 4, 1451-1455.
[48] 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.
[47] 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.
[46] Sharp asymptotic of solutions to some nonlocal parabolic equations.
(with A. Ghosh)
Discrete Contin. Dyn. Syst. 45 (2025), no. 4, 1297-1334.
[45] Extension problem for the fractional parabolic Lam\'e operator and unique continuation.
(with S. Senapati)
Calc. Var. Partial Differential Equations 63 (2024), no. 8, Paper No. 203.
[44] Higher order Boundary Schauder Estimates in Carnot Groups.
(with N. Garofalo and I. Munive)
Math Ann. 390 (2024), no. 4, 6013-6047.
[43] The Calderón problem for space-time fractional parabolic operators with variable coefficients.
(with S. Senapati)
SIAM J. Math. Anal. 56 (2024), no. 4, 4759-4810.
[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.