Renjin Jiang

activity

20092026

most citedHamilton's Gradient Estimates and A Monotonicity Formula for Heat Flows on Metric Measure Spaces

11 citations · 56 across the 24 of their papers we have counts for

collaborators

28 papers

math.CA2026

The Coulhon--Duong conjecture for the Riesz transform on complete Riemannian manifolds

Rui Chen, Renjin Jiang, Bo Li +1

Let $M$ be a complete, non-compact Riemannian manifold. We prove that its Riesz transform is of weak type $(1, 1)$ , with constant $2$ for real-valued functions. Consequently, it is…

math.AP2024

Some remarks on Riesz transform on exterior Lipschitz domains

Renjin Jiang, Sibei Yang

Let $n \geq 2$ and $L = - div (A \nabla \cdot)$ be an elliptic operator on $R^{n}$ . Given an exterior Lipschitz domain $Ω$ , let $L_{D}$ be the elliptic ope…

math.CA2022

Riesz transform on manifolds with ends of different volume growth for $1 < p < 2$

Renjin Jiang, Hongquan Li, Haibo Lin

Let $M_{1}$ , $\dots$ , $M_{ℓ}$ be complete, connected and non-collapsed manifolds of the same dimension, where $2 \leq ℓ \in N$ , and suppose that each $M_{i}$ satisfies a doub…

math.AP2022

Riesz transform on exterior Lipschitz domains and applications

Renjin Jiang, Fanghua Lin

Let $L = - div A \nabla$ be a uniformly elliptic operator on $R^{n}$ , $n \geq 2$ . Let $Ω$ be an exterior Lipschitz domain, and let $L_{D}$ and ${\maths…

math.CA2020

On the Dirichlet problem for the Schrödinger equation with boundary value in BMO space

Renjin Jiang, Bo Li

Let $(X, d, μ)$ be a metric measure space satisfying a $Q$ -doubling condition, $Q > 1$ , and an $L^{2}$ -Poincaré inequality. Let $L = L + V$ be a Schrödinger operator on $…

math.DG2018★ 3 cited

Riesz transform under perturbations via heat kernel regularity

Renjin Jiang, Fanghua Lin

Let $M$ be a complete non-compact Riemannian manifold. In this paper, we derive sufficient conditions on metric perturbation for stability of $L^{p}$ -boundedness of the Riesz transfo…

math.CA2018

Flow with $A_{\infty} (R)$ density and transport equation in $BMO (R)$

Renjin Jiang, Kangwei Li, Jie Xiao

We show that, if $b \in L^{1} (0, T; L_{loc}^{1} (R))$ has spatial derivative in the John-Nirenberg space $BMO (R)$ , then it generalizes a unique flow $ϕ(…

math.DG2017★ 3 cited

Riesz transform via heat kernel and harmonic functions on non-compact manifolds

Renjin Jiang

Let $M$ be a complete non-compact manifold satisfying the volume doubling condition, with doubling index $N$ and reverse doubling index $n$ , $n \leq N$ , both for large balls. Assume…

math.MG2017

Gradient estimates for heat kernels and harmonic functions

Thierry Coulhon, Renjin Jiang, Pekka Koskela +1

Let $(X, d, μ)$ be a doubling metric measure space endowed with a Dirichlet form $\E$ deriving from a "carré du champ". Assume that $(X,d,μ,\E)$ supports a scale-invariant $L^{2}$ -Poin…

math.CA2016

Korn's inequality and John domains

Renjin Jiang, Aapo Kauranen

It is quite well known that Korn's inequality is true on all John domains. We are interested in the converse implication under assumption of so called separation condition of the d…

math.MG2015★ 11 cited

Hamilton's Gradient Estimates and A Monotonicity Formula for Heat Flows on Metric Measure Spaces

Renjin Jiang, Huichun Zhang

In this paper, we extend the Hamilton's gradient estimates \cite{har93} and a monotonicity formula of entropy \cite{ni04} for heat flows from smooth Riemannian manifolds to (non-sm…

math.AP2015

A Note on Transport Equation in Quasiconformally Invariant Spaces

Albert Clop, Renjin Jiang, Joan Mateu +1

In this note, we study the well-posedness of the Cauchy problem for the transport equation in the BMO space and certain Triebel-Lizorkin spaces.

math.CA2015

Flows for non-smooth vector fields with subexponentially integrable divergence

Albert Clop, Renjin Jiang, Joan Mateu +1

In this paper, we study flows associated to Sobolev vector fields with subexponentially integrable divergence. Our approach is based on the transport equation following DiPerna-Lio…

math.AP2015★ 2 cited

Linear transport equations for vector fields with subexponentially integrable divergence

Albert Clop, Renjin Jiang, Joan Mateu +1

We face the well-posedness of linear transport Cauchy problems $$\begin{cases}\dfrac{\partial u}{\partial t} + b\cdot\nabla u + c\,u = f&(0,T)\times{\mathbb R}^n\\u(0,\cdot)=u_0\in…

math.MG2014★ 7 cited

Heat Kernel Bounds on Metric Measure Spaces and Some Applications

Renjin Jiang, Huaiqian Li, Huichun Zhang

Let $(X, d, μ)$ be a $R C D^{*} (K, N)$ space with $K \in R$ and $N \in [1, \infty]$ . For $N \in [1, \infty)$ , we derive the upper and lower bounds of the heat kernel on $(X, d, μ)$ …

math.MG2014★ 3 cited

The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces

Renjin Jiang

Let $(X, d, μ)$ be a $R C D^{*} (K, N)$ space with $K \in ma t hbb R$ and $N \in [1, \infty)$ . Suppose that $(X, d)$ is connected, complete and separable, and $\supp μ=X$. We prove that the…

math.AP2013★ 3 cited

Towards spaces of harmonic functions with traces in square Campanato space and its scaling invariant

Renjin Jiang, Jie Xiao, Dachun Yang

For $n \geq 1$ and $α \in (- 1, 1)$ , let $H^{α, 2}$ be the space of harmonic functions $u$ on the upper half space $R_{+}^{n + 1}$ satisfying $$\displaystyle\sup_{(x_0,r)\in \mathbb…

math.MG2013★ 5 cited

Cheeger-harmonic functions in metric measure spaces revisited

Renjin Jiang

Let $(X, d, μ)$ be a complete metric measure space, with $μ$ a locally doubling measure, that supports a local weak $L^{2}$ -Poincaré inequality. By assuming a heat semigroup type curva…

math.CA2013★ 1 cited

Solvability of the divergence equation implies John via Poincaré inequality

Renjin Jiang, Aapo Kauranen, Pekka Koskela

Let $Ω\subset \rr^2$ be a bounded simply connected domain. We show that, for a fixed (every) $p\in (1,\fz),$ the divergence equation $div v = f$ is solvable in $W^…

math.CA2013★ 1 cited

Korn inequality on irregular domains

Renjin Jiang, Aapo Kauranen

In this paper, we study the weighted Korn inequality on some irregular domains, e.g., $s$ -John domains and domains satisfying quasi-hyperbolic boundary conditions. Examples regardi…

math.FA2013★ 2 cited

Hajlasz Gradients Are Upper Gradients

Renjin Jiang, Nageswari Shanmugalingam, Dachun Yang +1

Let $(X, d, μ)$ be a metric measure space, with $μ$ a Borel regular measure. In this paper, we prove that, if $u \in L_{loc}^{1} (X)$ and $g$ is a Hajłasz gradient…

math.AP2013

Regularity and Capacity for the Fractional Dissipative Operator

Renjin Jiang, Jie Xiao, Dachun Yang +1

This note is devoted to exploring some analytic-geometric properties of the regularity and capacity associated to the so-called fractional dissipative operator $\partial_{t} + (- Δ)^{α}$ ,…

math.AP2011★ 1 cited

Gradient Estimate for Solutions to Poisson Equations in Metric Measure Spaces

Renjin Jiang

Let $(X, d)$ be a complete, pathwise connected metric measure space with locally Ahlfors $Q$ -regular measure $μ$ , where $Q > 1$ . Suppose that $(X, d, μ)$ supports a (local) $(1, 2)$ -Poin…

math.AP2010★ 4 cited

Lipschitz continuity of solutions of Poisson equations in metric measure spaces

Renjin Jiang

Let $(X, d)$ be a pathwise connected metric space equipped with an Ahlfors $Q$ -regular measure $μ$ , $Q \in [1, \infty)$ . Suppose that $(X, d, μ)$ supports a 2-Poincaré inequality and a S…

The Coulhon--Duong conjecture for the Riesz transform on complete Riemannian manifolds

Some remarks on Riesz transform on exterior Lipschitz domains

Riesz transform on manifolds with ends of different volume growth for 1<p<2

Riesz transform on exterior Lipschitz domains and applications

On the Dirichlet problem for the Schrödinger equation with boundary value in BMO space

Riesz transform under perturbations via heat kernel regularity

Flow with A∞​(R) density and transport equation in BMO(R)

Riesz transform via heat kernel and harmonic functions on non-compact manifolds

Gradient estimates for heat kernels and harmonic functions

Korn's inequality and John domains

Hamilton's Gradient Estimates and A Monotonicity Formula for Heat Flows on Metric Measure Spaces

A Note on Transport Equation in Quasiconformally Invariant Spaces

Flows for non-smooth vector fields with subexponentially integrable divergence

Linear transport equations for vector fields with subexponentially integrable divergence

Heat Kernel Bounds on Metric Measure Spaces and Some Applications

The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces

Towards spaces of harmonic functions with traces in square Campanato space and its scaling invariant

Cheeger-harmonic functions in metric measure spaces revisited

Solvability of the divergence equation implies John via Poincaré inequality

Korn inequality on irregular domains

Hajlasz Gradients Are Upper Gradients

Regularity and Capacity for the Fractional Dissipative Operator

Gradient Estimate for Solutions to Poisson Equations in Metric Measure Spaces

Lipschitz continuity of solutions of Poisson equations in metric measure spaces

Riesz transform on manifolds with ends of different volume growth for $1 < p < 2$

Flow with $A_{\infty} (R)$ density and transport equation in $BMO (R)$