论文标题
有界域上的非本地半球向量操作员：庞加莱的不平等及其应用
Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications
论文作者
论文摘要
这项工作有助于非局部矢量积分作为一种不可或缺的数学工具，用于研究在各种应用中出现的非本地模型。我们定义了具有一般核函数的非本地半球梯度，差异和卷曲算子（具有有限或无限支持的分数或分数类型），并研究相关的非局部矢量身份。我们研究了与零dirichlet边界条件和半球梯度操作员相关的有界域上的非局部功能空间，并表明它是一个可分离的希尔伯特空间，其中具有光滑的功能。一个主要结果是基于一些应用的非局部庞加莱不平等现象，其中包括对非局部对流扩散的应用，线性弹性的非本地对应模型以及在有限域中的非局部Helmholtz分解。
This work contributes to nonlocal vector calculus as an indispensable mathematical tool for the study of nonlocal models that arises in a variety of applications. We define the nonlocal half-ball gradient, divergence and curl operators with general kernel functions (integrable or fractional type with finite or infinite supports) and study the associated nonlocal vector identities. We study the nonlocal function space on bounded domains associated with zero Dirichlet boundary conditions and the half-ball gradient operator and show it is a separable Hilbert space with smooth functions dense in it. A major result is the nonlocal Poincaré inequality, based on which a few applications are discussed, and these include applications to nonlocal convection-diffusion, nonlocal correspondence model of linear elasticity, and nonlocal Helmholtz decomposition on bounded domains.
