Zobrazeno 1 - 10
of 50
pro vyhledávání: '"Gu, Qingsong"'
Autor:
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 Laplacian is defined through a strongly recurrent self-similar local regular Dirichlet form. For
Externí odkaz:
http://arxiv.org/abs/2409.01623
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 to a nonlocal elliptic inequality \begin{equation*} (-\Delta)^{\alpha} u\geq u^{q}\sigma\qua
Externí odkaz:
http://arxiv.org/abs/2304.02808
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 semi-linear elliptic inequality \begin{equation*} \Delta u+u^{\sigma}\leq0\quad \text{in}\,\,V, \end
Externí odkaz:
http://arxiv.org/abs/2201.06397
Autor:
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 extend the results due to Bourgain-Brezis-Mironescu(BBM) and Maz'ya-Shaposhnikova(MS) respecti
Externí odkaz:
http://arxiv.org/abs/2201.00353
We study $p$-energies on post critically finite (p.c.f.) self-similar sets for $1
Externí odkaz:
http://arxiv.org/abs/2112.10932
Autor:
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 $C^{\infty}_c(\mathbb{R}^N)$. The formula was obtained by replacing the $L^p(\mathbb{R}^{2N})$ norm in the Gagliardo semi-
Externí odkaz:
http://arxiv.org/abs/2102.09657
Autor:
Gu, Qingsong, Huang, Qingzhong
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 September 2023 525(2)
We reinvestigate nonexistence and existence of global positive solutions to heat equation with a potential term on Riemannian manifolds. Especially, we give a very natural sharp condition only in terms of the volume of geodesic ball to obtain nonexis
Externí odkaz:
http://arxiv.org/abs/1901.01518
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 obtain the two-sided sub-Gaussian heat kernel estimates of time change of the standard diffusion
Externí odkaz:
http://arxiv.org/abs/1806.02947
Publikováno v:
In Advances in Mathematics 27 August 2022 405