In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application ...In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application of the estimate, we also obtained slight improvements of Davies' Li-Yau-type gradient estimate.展开更多
We present some improvements of the Li-Yau heat kernel estimate on a Riemannian manifold with Ricci curvature bounded below.As a consequence we prove a gradient estimate to the heat kernel with an optimal leading term.
Let （M, g） be a complete noncompact Riemannian manifold. In this note, we derive a local Hamilton-type gradient estimate for positive solution to a simple nonlinear parabolic equationon tu=△u＋aulogu＋qu on M ...Let （M, g） be a complete noncompact Riemannian manifold. In this note, we derive a local Hamilton-type gradient estimate for positive solution to a simple nonlinear parabolic equationon tu=△u＋aulogu＋qu on M × （0, ∞）, where a is a constant and q is a C2 function. This result can be compared with the ones of Ma （JFA, 241, 374-382 （2006）） and Yang （PAMS, 136, 4095-4102 （2008））. Also, we obtain Hamilton＇s gradient estimate for the Schodinger equation. This can be compared with the result of Ruan （JGP, 58, 962-966 （2008））.展开更多
In this paper, let(M~n, g) be an n-dimensional complete Riemannian manifold with the mdimensional Bakry–mery Ricci curvature bounded below. By using the maximum principle, we first prove a Li–Yau type Harnack differ...In this paper, let(M~n, g) be an n-dimensional complete Riemannian manifold with the mdimensional Bakry–mery Ricci curvature bounded below. By using the maximum principle, we first prove a Li–Yau type Harnack differential inequality for positive solutions to the parabolic equation u= LF(u)=ΔF(u)-f·F(u),on compact Riemannian manifolds Mn, where F∈C~2(0, ∞), F>0 and f is a C~2-smooth function defined on M~n. As application, the Harnack differential inequalities for fast diffusion type equation and porous media type equation are derived. On the other hand, we derive a local Hamilton type gradient estimate for positive solutions of the degenerate parabolic equation on complete Riemannian manifolds. As application, related local Hamilton type gradient estimate and Harnack inequality for fast dfiffusion type equation are established. Our results generalize some known results.展开更多
基金partially supported by the Yangfan project from Guangdong ProvinceNSFC(11571215)
文摘In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application of the estimate, we also obtained slight improvements of Davies' Li-Yau-type gradient estimate.
基金Supported by National Natural Science Foundation of China(Grant Nos.11926339,11821101)。
文摘We present some improvements of the Li-Yau heat kernel estimate on a Riemannian manifold with Ricci curvature bounded below.As a consequence we prove a gradient estimate to the heat kernel with an optimal leading term.
文摘Let （M, g） be a complete noncompact Riemannian manifold. In this note, we derive a local Hamilton-type gradient estimate for positive solution to a simple nonlinear parabolic equationon tu=△u＋aulogu＋qu on M × （0, ∞）, where a is a constant and q is a C2 function. This result can be compared with the ones of Ma （JFA, 241, 374-382 （2006）） and Yang （PAMS, 136, 4095-4102 （2008））. Also, we obtain Hamilton＇s gradient estimate for the Schodinger equation. This can be compared with the result of Ruan （JGP, 58, 962-966 （2008））.
基金Supported by Universities Natural Science Foundation of Anhui Province(Grant No.KJ2016A310)
文摘In this paper, let(M~n, g) be an n-dimensional complete Riemannian manifold with the mdimensional Bakry–mery Ricci curvature bounded below. By using the maximum principle, we first prove a Li–Yau type Harnack differential inequality for positive solutions to the parabolic equation u= LF(u)=ΔF(u)-f·F(u),on compact Riemannian manifolds Mn, where F∈C~2(0, ∞), F>0 and f is a C~2-smooth function defined on M~n. As application, the Harnack differential inequalities for fast diffusion type equation and porous media type equation are derived. On the other hand, we derive a local Hamilton type gradient estimate for positive solutions of the degenerate parabolic equation on complete Riemannian manifolds. As application, related local Hamilton type gradient estimate and Harnack inequality for fast dfiffusion type equation are established. Our results generalize some known results.
