AI 中文总结
针对n维欧几里得空间有界光滑区域上的半阶狄拉克算子及其幂的边值问题，证明其解为半阶希尔伯特空间中的广义函数，由两类积分解正交和构成，并采用特定符号表示正交和。
AI 中文摘要
给定n维欧几里得空间中的一个有界光滑区域，考虑半阶狄拉克算子及其幂的边值问题，其中f是区域内解的半导数的值，g是解在边界上的迹值。我们将证明，该解是半阶希尔伯特空间中的广义函数u，它由两部分正交和构成：一部分是从分数阶半狄拉克算子的区域值产生的区域积分解，另一部分是从解的边界或迹值产生的边界积分解。我们使用两个不同的符号来表示索伯列夫空间的子空间及正交子空间中函数的正交和。
英文摘要
Let a bounded and smooth domain in the n dimensional Euclidean space be given and consider a boundary value problem of the half order Dirac operator and its power, with f be the value of the half derivative of the solution in the domain and, g be the trace value of the solution over the boundary. We will show that the solution will be a generalized function u in the half order Hilbert space which is the orthogonal sum of the solution that emerged as a domain integral from the domain value of the fractional half Dirac operator and the one that is the boundary integrals that emerges from the boundary or trace value of the solution. We use two different symbols to designate orthogonal sums for subspaces and functions in orthogonal subspaces of the Sobolev space.
Comments21 pages results on fractional half Dirac operator over Sobolev spaces
