论文标题
分数运算符的傅立叶方法
Fourier methods for fractional-order operators
论文作者
论文摘要
这是一项关于使用傅立叶变换方法在处理边界问题的调查的调查，用于分数laplacian $（-δ）^a $（0 <a <1），以及在$ r^n $中的有限的开放式$ω$上。演示开始于基础级别。详细说明了两个点：1）$ d^a $（$ d（x）= dist（x，dΩ）$，如何出现在图片中，这与均质dirichlet问题的精确解决方案空间是所谓的A传递空间。 2）局部非均匀的dirichlet条件的自然定义$γ_0（u/d^{a-1}）=φ$。我们还简要介绍了一些进一步的发展：进化问题（对于$ d_t u -r^+pu = f（x，t）$）和解决问题（对于$ pu -λu= f $），也有非零边界条件。零件的集成，格林的公式。
This is a survey on the use of Fourier transformation methods in the treatment of boundary problems for the fractional Laplacian $(-Δ)^a$ (0<a<1), and pseudodifferential generalizations P, over a bounded open set $Ω$ in $R^n$. The presentation starts at an elementary level. Two points are explained in detail: 1) How the factor $d^a$, with $d(x)=dist(x,dΩ)$, comes into the picture, related to the fact that the precise solution spaces for the homogeneous Dirichlet problem are so-called a-transmission spaces. 2) The natural definition of a local nonhomogeneous Dirichlet condition $γ_0(u/d^{a-1})=φ$. We also give brief accounts of some further developments: Evolution problems (for $d_t u - r^+Pu = f(x,t)$) and resolvent problems (for $Pu-λu=f$), also with nonzero boundary conditions. Integration by parts, Green's formula.
