We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved. Such problems respectively lead to anomalous behavior on the bulk and on the surface of a given domain. Such a behavior can be considered (in a macroscopic viewpoint) in order to describe regular motion on irregular domains (in the microscopic viewpoint).

翻译：我们简短地介绍了有关非本地运营商和非正规域的新和众所周知的事实,在涉及非本地运营商时,会考虑棘手的问题和边界价值问题,这些问题分别导致某一域的散装和表面异常行为。 这种行为可以(从宏观角度)考虑,以便描述在非正规域(从微观角度)的定期运动。