锥中分数拉普拉斯算子的热核

各向异性分数拉普拉斯算子的势核估计和Harnack不等式

Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplacian

利用正最大值原理刻画了一类齐次平移不变对称非局部算子，其调和函数满足Harnack不等式.我们还估计了相应的半群和势核。

Dirichlet条件下分数阶Laplacian算子的热核估计

Heat kernel estimates for the fractional Laplacian with Dirichlet conditions

本文对包括Lipschitz域在内的一类一般域给出了具有Dirichlet条件的分数Laplacian的热核的精确估计。

窄锥上分数拉普拉斯算子的Martin核

Martin kernel for fractional Laplacian in narrow cones

给出了当锥角趋于零时，分式拉普拉斯算子的Martin核的齐次度的幂律。

Heat kernel of fractional Laplacian with Hardy drift via desingularizing weights

We establish sharp two-sided bounds on the heat kernel of the fractional Laplacian, perturbed by a drift having critical-order singularity, by transferring it to appropriate weighted space with singular weight.

Semilinear equations for non-local operators: beyond the fractional Laplacian

We study semilinear problems in general bounded open sets for non-local operators with exterior and boundary conditions. The operators are more general than the fractional Laplacian. We also give results in case of bounded $C^{1,1}$ open sets.

Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradient

By using Duhamel's formula, we prove sharp two-sided estimates for the heat kernel of spectral fractional Laplacian with time-dependent gradient perturbation in bounded $C^{1,1}$ domains. Moreover, we also obtain gradient estimate as well as Hölder continuity of the gradient of the heat kernel.

梯度扰动下分数阶Laplacian的格林函数估计

Estimates of the Green function for the fractional Laplacian perturbed by gradient

对于有界光滑多维开集，如果漂移函数在适当的Kato类中，则阶数大于1的分数阶Laplacian的格林函数与其梯度扰动的格林函数是可比的.

具有大不可压漂移的分数阶拉普拉斯算子的主函数eigenvalue

Principal eigenvalue of the fractional Laplacian with a large incompressible drift

在有界光滑区域上的分数阶拉普拉斯算子上增加一个无发散漂移，讨论了狄利克雷问题的主特征值的性质.当且仅当漂移在分数拉普拉斯算子的二次型域中具有非平凡的首次积分时，本征值保持有界。

锥上的Heat Equation与球面Laplacian的谱

Heat Equation on the Cone and the Spectrum of the Spherical Laplacian

从锥上热传导方程的角度分析了球域上拉普拉斯算子的谱。热方程在锥上的级数解是已知的，导致在更高维度的领域上的拉普拉斯本征值问题的研究。它发现，解决方案自然导致一个谱函数，一个'生成函数'的特征值和多重性的拉普拉斯算子，表达在封闭形式的某些领域的领域。谱函数的分析性质提出了一个简单的缩放过程估计的特征值。比较第一特征值估计与现有的理论和数值计算结果的一些特定的区域显示出显着的协议。

Interior estimates for the eigenfunctions of the fractional Laplacian on a bounded Euclidean domain

This paper is devoted to interior, i.e. away from the boundary, estimates for eigenfunctions of the fractional Laplacian in an Euclidean domain of $\mathbb R^d$.

Fractional Laplacian with Hardy potential

We give sharp two-sided estimates of the semigroup generated by the fractional Laplacian plus the Hardy potential on $\mathbb{R}^d$, including the case of the critical constant. We use Davies' method back-to-back with a new method of integral analysis of Duhamel's formula.

Poincaré type and spectral gap inequalities with fractional Laplacians on Hamming cube

We prove here some dimension free Poincaré-type inequalities on Hamming cube for functions with different spectral properties and for fractional Laplacians. In this note the main attention is paid to estimates in $L^1$ norm on Hamming cube. We build the examples showing that our assumptions on spectral properties of functions cannot be dropped in general.