Search Results - "Gu, Qingsong"

Semi-linear elliptic inequalities on weighted graphs by Gu, Qingsong, Huang, Xueping, Sun, Yuhua

“…Let ( V , μ ) be an infinite, connected, locally finite weighted graph. We study the problem of existence or non-existence of positive solutions to a…”
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Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold by Gu, Qingsong, Sun, Yuhua, Xiao, Jie, Xu, Fanheng

“…This paper determines when the Cauchy problem ∂ t u = Δ u - V u + W u p in M × ( 0 , ∞ ) u ( · , 0 ) = u 0 ( · ) in M has no global positive solution on a…”
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Homogeneous Dirichlet Forms on p.c.f. Fractals and their Spectral Asymptotics by Gu, Qingsong, Lau, Ka-Sing, Qiu, Hua

“…We formulate a class of “homogeneous” Dirichlet forms (DF) that aims to explore those forms that do not satisfy the conventional energy self-similar identity…”
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Geodesic metrics on fractals and applications to heat kernel estimates by Gu, Qingsong, Lau, Ka-Sing, Qiu, Hua, Ruan, Huo-Jun

“…It is well known that for a Brownian motion, if we change the medium to be inhomogeneous by a measure μ , then the new motion (the time-changed process) will…”
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Anisotropic versions of the Brezis-Van Schaftingen-Yung approach at s = 1 and s = 0 by Gu, Qingsong, Huang, Qingzhong

“…In 2014, Ludwig showed the limiting behavior of the anisotropic Gagliardo s-seminorm of a function f as s→1− and s→0+, which extend the results due to…”
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p-energies on p.c.f. self-similar sets by Cao, Shiping, Gu, Qingsong, Qiu, Hua

“…We study p-energies on post-critically finite (p.c.f.) self-similar sets for 1<p<∞, as limits of discrete p-energies on approximation graphs, extending the…”
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A new formula for the Lp norm by Gu, Qingsong, Yung, Po-Lam

“…Recently, Brezis, Van Schaftingen and the second author [4] established a new formula for the W˙1,p norm of a function in Cc∞(RN). The formula was obtained by…”
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A new formula for the L norm by Gu, Qingsong, Yung, Po-Lam

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Prediction of microsatellite instability of colorectal cancer using multi-scale pathological images based on deep learning by Cao, Ruifen, Gu, Qingsong, Tan, Dayu, Wei, Pijing, Zheng, Chunhou

“…Immunotherapy is an excellent treatment option for many solid tumors, and the therapeutic effect has been proved in clinical. Microsatellite instability (MSI)…”
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BGD domains in p.c.f. self-similar sets I: boundary value problems for harmonic functions by Gu, Qingsong, Qiu, Hua

“…We study the boundary value problems for harmonic functions on open connected subsets of post-critically finite (p.c.f.) self-similar sets, on which the…”
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Anisotropic versions of the Brezis-Van Schaftingen-Yung approach at $s=1$ and $s=0 by Gu, Qingsong, Huang, Qingzhong

“…In 2014, Ludwig showed the limiting behavior of the anisotropic Gagliardo $s$-seminorm of a function $f$ as $s\rightarrow 1^-$ and $s\rightarrow0^+$, which…”
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Sharp criteria for nonlocal elliptic inequalities on manifolds by Gu, Qingsong, Huang, Xueping, Sun, Yuhua

“…Let $M$ be a complete non-compact Riemannian manifold and $\sigma $ be a Radon measure on $M$, we study the existence and non-existence of positive solutions…”
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A new formula for the $L^p$ norm by Gu, Qingsong, Yung, Po-Lam

“…Recently, Brezis, Van Schaftingen and the second author established a new formula for the $\dot{W}^{1,p}$ norm of a function in $C^{\infty}_c(\mathbb{R}^N)$…”
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Superlinear elliptic inequalities on weighted graphs by Gu, Qingsong, Huang, Xueping, Sun, Yuhua

“…Let $(V,\mu)$ be an infinite, connected, locally finite weighted graph. We study the problem of existence or non-existence of positive solutions to a…”
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p$-energies on p.c.f. self-similar sets by Cao, Shiping, Gu, Qingsong, Qiu, Hua

“…We study $p$-energies on post critically finite (p.c.f.) self-similar sets for $1<p<\infty$, as limits of discrete $p$-energies on approximation graphs,…”
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Lipschitz invariance of walk dimension on connected self-similar sets by Rao, Hui, Gu, Qingsong

“…Walk dimension is an important conception in analysis of fractals. In this paper we prove that the walk dimension of a connected compact set possessing an…”
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On nonexistence and existence of positive global solutions to heat equation with a potential term on Riemannian manifolds by Gu, Qingsong, Sun, Yuhua, Xu, Fanheng

“…We reinvestigate nonexistence and existence of global positive solutions to heat equation with a potential term on Riemannian manifolds. Especially, we give a…”
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Dirichlet forms and critical exponents on fractals by Gu, Qingsong, Lau, Ka-Sing

“…Let $B^{\sigma}_{2, \infty}$ denote the Besov space defined on a compact set $K \subset {\Bbb R}^d$ which is equipped with an $\alpha$-regular measure $\mu$…”
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Metrics on the Sierpinski carpet by weight functions by Gu, Qingsong, Qiu, Hua, Ruan, Huo-Jun

“…We construct certain metrics on the Sierpinski carpet via a class of self-similar weight functions. Using these metrics and by applying known results, we…”
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On a recursive construction of Dirichlet form on the Sierpi\'nski gasket by Gu, Qingsong, Lau, Ka-Sing, Qiu, Hua

“…Let $\Gamma_n$ denote the $n$-th level Sierpi\'nski graph of the Sierpi\'nski gasket $K$. We consider, for any given conductance $(a_0, b_0, c_0)$ on…”
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