论文标题
限制的非本地操作员将拉普拉斯和分数拉普拉斯桥桥接在一起
A restricted nonlocal operator bridging together the Laplacian and the Fractional Laplacian
论文作者
论文摘要
在这项工作中，我们介绍了涉及非本地运算符$（δ）_Δ^{s} $的体积约束问题，与分数laplacian $（ - δ）^{s} $密切相关，并取决于参数$δ> 0 $ nofor。我们研究相关的线性和光谱问题以及这些体积约束问题的行为，当时$δ\ to to to \ to0^+$和$δ\ to+\ infty $。通过这些限制过程$（ - δ）_δ^{s} $，我们分别将光谱收敛到本地laplacian和分数laplacian作为$δ\ to 0^ +$和$δ\ to +Δ\ to +\ to +\ to +\ to +\ iffty $，并且我们证明了这些问题的问题$（$）的解决方案$（$）$（$）的解决方案$（ $δ\ to0^+$或涉及$（-Δ）^s $的非本地分数dirichlet问题的解决方案，为$δ\ to+\ infty $。
In this work we introduce volume constraint problems involving the nonlocal operator $(-Δ)_δ^{s}$, closely related to the fractional Laplacian $(-Δ)^{s}$, and depending upon a parameter $δ>0$ called horizon. We study the associated linear and spectral problems and the behavior of these volume constraint problems when $δ\to0^+$ and $δ\to+\infty$. Through these limit processes on $(-Δ)_δ^{s}$ we derive spectral convergence to the local Laplacian and to the fractional Laplacian as $δ\to 0^+$ and $δ\to +\infty$ respectively, as well as we prove the convergence of solutions of these problems to solutions of a local Dirichlet problem involving $(-Δ)$ as $δ\to0^+$ or to solutions of a nonlocal fractional Dirichlet problem involving $(-Δ)^s$ as $δ\to+\infty$.
