Isidro H. Munive

activity

20102022

collaborators

11 papers

math.AP2022

Borderline gradient continuity for the normalized $p$ -parabolic operator

Murat Akman, Agnid Banerjee, Isidro H. Munive

In this paper, we prove gradient continuity estimates for viscosity solutions to $Δ_{p}^{N} u - u_{t} = f$ in terms of the scaling critical $L (n + 2, 1)$ norm of $f$ , where $Δ_{p}^{N}$ is th…

math.AP2022

Higher order Boundary Schauder Estimates in Carnot Groups

Agnid Banerjee, Nicola Garofalo, Isidro H. Munive

In his seminal 1981 study D. Jerison showed the remarkable negative phenomenon that there exist, in general, no Schauder estimates near the characteristic boundary in the Heisenber…

math.AP2019

The Harnack inequality for a class of nonlocal parabolic equations

Agnid Banerjee, Nicola Garofalo, Isidro H. Munive +1

In this paper we establish a scale invariant Harnack inequality for the fractional powers of parabolic operators $(\partial_{t} - L)^{s}$ , $0 < s < 1$ , where $L$ is the…

math.AP2019

Gradient continuity estimates for the normalized $p$ -Poisson equation

Agnid Banerjee, Isidro H. Munive

In this paper, we obtain gradient continuity estimates for viscosity solutions of $Δ_{p}^{N} u = f$ in terms of the scaling critical $L (n, 1)$ norm of $f$ , where $Δ_{p}^{N}$ is the norm…

math.AP2018

Solutions of the Yamabe Equation By Lyapunov-Schmidt Reduction

Jorge Davila, Isidro H. Munive

Given any closed Riemannian manifold $(M, g)$ we use the Lyapunov-Schmidt finite-dimensional reduction method and the classical Morse and Lusternick-Schnirelmann theories to prove m…

math.AP2018

Compactness methods for $Γ^{1, α}$ boundary Schauder estimates in Carnot groups

Agnid Banerjee, Nicola Garofalo, Isidro Munive

The aim of this paper is to prove $Γ^{1, α}$ Schauder estimates near a $C^{1, α}$ non-characteristic portion of the boundary for $Γ^{0, α}$ perturbations of horizontal Laplaceans in…

math.DG2016

Sub-Riemannian curvature of Carnot groups with rank-two distributions

Isidro H. Munive

The notion of curvature discussed in this paper is a far going generalization of the Riemannian sectional curvature. It was first introduced by Agrachev, Barilari and Rizzi in arXi…

math.AP2016

Estimates of the Green function and the initial-Dirichlet problem for the heat equation in sub-Riemannian spaces

Nicola Garofalo, Isidro H. Munive

In a cylinder $D_{T} = Ω \times (0, T)$ , where $Ω \subset R^{n}$ , we examine the relation between the $L$ -caloric measure, $d ω^{(x, t)}$ , where $L$ is the heat operator associated…

math.DG2012

Volume and distance comparison theorems for sub-Riemannian manifolds

Fabrice Baudoin, Michel Bonnefont, Nicola Garofalo +1

In this paper we study global distance estimates and uniform local volume estimates in a large class of sub-Riemannian manifolds. Our main device is the generalized curvature dimen…

math.AP2010

Non-divergence form parabolic equations associated with non-commuting vector fields: Boundary behavior of nonnegative solutions

M. Frentz, N. Garofalo, E. Götmark +2

In a cylinder $Ω_{T} = Ω \times (0, T) \subset R_{+}^{n + 1}$ we study the boundary behavior of nonnegative solutions of second order parabolic equations of the form \[ Hu =\sum_{i,j=1}^ma_{…

math.AP2010

Boundary Behavior of Non-Negative Solutions of the Heat Equation in Sub-Riemannian Spaces

Isidro H Munive

We prove Fatou type theorems for solutions of the heat equation in sub- Riemannian spaces. The doubling property of L-caloric measure, the Dahlberg estimate, the local comparison t…

Borderline gradient continuity for the normalized p-parabolic operator