4 papers
A parabolic analogue of the higher-order comparison theorem of De Silva and Savin
Agnid Banerjee, Nicola Garofalo
We show that the quotient of two caloric functions which vanish on a portion of the lateral boundary of a domain is up to the boundary for . In the…
Modica type gradient estimates for reaction-diffusion equations and a parabolic counterpart of a conjecture of De Giorgi
Agnid Banerjee, Nicola Garofalo
We continue the study of Modica type gradient estimates for non-homogeneous parabolic equations initiated in \cite{BG}. First, we show that for the parabolic minimal surface equati…
Modica type gradient estimates for an inhomogeneous variant of the normalized p-laplacian evolution
Agnid Banerjee, Nicola Garofalo
In this paper, we study an inhomogeneous variant of the normalized -Laplacian evolution which has been recently treated in \cite{BG1}, \cite{Do}, \cite{MPR} and \cite{Ju}. We sh…
Gradient bounds and monotonicity of the energy for some nonlinear singular diffusion equations
Agnid Banerjee, Nicola Garofalo
We construct viscosity solutions to the nonlinear evolution equation \eqref{p} below which generalizes the motion of level sets by mean curvature (the latter corresponds to the cas…