Renjin Jiang

Fractional Riesz Transforms and Applications on Exterior Domains

Renjin Jiang, Tianjun Shen, Sibei Yang, Houkun Zhang

cn (code pays fourni par la source)

Pólya's Conjecture Up to ε‐loss and Quantitative Estimates for the Remainder of Weyl's Law

Renjin Jiang, Fanghua Lin

ABSTRACT Let be a bounded Lipschitz domain. For any we show that for any Dirichlet eigenvalue , it holds, where, is given explicitly. This reduces the ‐loss version of Pólya's conjecture to a computational problem. This estimate is based on quantitative estimates …

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The improved Berezin-Li-Yau inequality and Kröger inequality and consequences

Zaihui Gan, Renjin Jiang, Fanghua Lin

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Sharp estimates for the heat kernel on exterior planar domains

Renjin Jiang, Tianjun Shen, Sibei Yang, Houkun Zhang

cn (code pays fourni par la source)

Riesz Transform on Manifolds with Ends of Different Volume Growth for $$1<p<2$$

Renjin Jiang, Hong-Quan Li, Haibo Lin

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Heat kernel estimates, fractional Riesz transforms and applications on exterior domains

Renjin Jiang, Tianjun Shen, Sibei Yang, Houkun Zhang

In this paper, we derive sharp two side heat kernel estimate on exterior $C^{1,1}$ domains in the plane, and sharp upper heat kernel bound on exterior $C^{1,\mathrm{Dini}}$ domains in $\mathbb{R}^n$, $n\ge 2$. Estimates for Green's function and Riesz potentials on exterior domains …

Some remarks on Riesz transforms on exterior Lipschitz domains

Renjin Jiang, Sibei Yang

Abstract Let $n\ge 2$ and $\mathcal {L}=-\mathrm {div}(A\nabla \cdot )$ be an elliptic operator on $\mathbb {R}^n$ . Given an exterior Lipschitz domain $\Omega $ , let $\mathcal {L}_D$ be the elliptic operator $\mathcal {L}$ on $\Omega $ subject to the Dirichlet …

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Riesz transform on exterior Lipschitz domains and applications

Renjin Jiang, Fanghua Lin

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Some remarks on Riesz transform on exterior Lipschitz domains

Renjin Jiang, Sibei Yang

Let $n\ge2$ and $\mathcal{L}=-\mathrm{div}(A\nabla\cdot)$ be an elliptic operator on $\mathbb{R}^n$. Given an exterior Lipschitz domain $Ω$, let $\mathcal{L}_D$ be the elliptic operator $\mathcal{L}$ on $Ω$ subject to the Dirichlet boundary condition. Previously it was known that the Riesz operator $\nabla \mathcal{L}_D^{-1/2}$ is …

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

Renjin Jiang, Hong-Quan Li, Haibo Lin

Let $M_1$, $\cdots$, $M_\ell$ be complete, connected and non-collapsed manifolds of the same dimension, where $2\le \ell\in\mathbb{N}$, and suppose that each $M_i$ satisfies a doubling condition and a Gaussian upper bound for the heat kernel. If each manifold $M_i$ has volume growth …

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

Renjin Jiang, Bo Li

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Riesz transform on exterior Lipschitz domains and applications

Renjin Jiang, Fanghua Lin

Let ${\mathscr{L}}=-\text{div}A\nabla$ be a uniformly elliptic operator on $\mathbb{R}^n$, $n\ge 2$. Let $Ω$ be an exterior Lipschitz domain, and let ${\mathscr{L}}_D$ and ${\mathscr{L}}_N$ be the operator ${\mathscr{L}}$ on $Ω$ subject to the Dirichlet and Neumann boundary values, respectively. We establish the boundedness …