论文标题
Rellich-Kondrachov定理的概括和不规则和分形边界框架中的痕量紧凑性
Generalization of Rellich-Kondrachov theorem and trace compacteness in the framework of irregular and fractal boundaries
论文作者
论文摘要
我们介绍了功能分析的最新结果调查，该调查允许在具有不规则边界的大型域中求解PDE。我们扩展了先前介绍的可允许域的概念，该域在域上具有D-SET边界，并具有该度量不一定是常规D量的边界。这给出了Rellich-Kondrachov定理的概括和痕量操作员的紧凑性，从而获得了常规经典案例，即在Robin边界条件下的Poisson边界有价值问题的弱解决方案的单位/存在，并获得了相关光谱问题的常规特性。
We present a survey of recent results of the functional analysis allowing to solve PDEs in a large class of domains with irregular boundaries. We extend the previously introduced concept of admissible domains with a d-set boundary on the domains with the boundaries on which the measure is not necessarily Ahlfors regular d-measure. This gives a generalization of Rellich-Kondrachov theorem and the compactness of the trace operator, allowing to obtain, as for a regular classical case the unicity/existence of weak solutions of Poisson boundary valued problem with the Robin boundary condition and to obtain the usual properties of the associated spectral problem.
