We study the asymptotic behavior of anomalous fractional diffusion processes in bad domains via the convergence of the associated energy forms. We introduce the associated Robin–Venttsel’ problems for the regional fractional Laplacian. We provide a suitable notion of fractional normal derivative on irregular sets via a fractional Green formula as well as existence and uniqueness results for the solution of the Robin–Venttsel’ problem by a semigroup approach. Submarkovianity and ultracontractivity properties of the associated semigroup are proved.

中文翻译：

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扩展域中分数阶扩散过程的收敛性

我们通过相关能量形式的收敛研究了坏域中异常分数扩散过程的渐近行为。我们介绍了有关区域分数拉普拉斯算子的罗宾–温特塞尔问题。我们通过分数Green公式提供不规则集上分数正导数的适当概念，以及通过半群方法解决Robin-Venttsel问题的存在性和唯一性结果。证明了相关半群的亚马尔科夫性和超收缩性。