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Mathematics > Analysis of PDEs

arXiv:2210.02327 (math)
[Submitted on 5 Oct 2022 (v1), last revised 27 Oct 2022 (this version, v2)]

Title:On the non-local boundary value problem from the probabilistic viewpoint

Authors:Mirko D'Ovidio
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Abstract: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).
Subjects: Analysis of PDEs (math.AP); Probability (math.PR); Statistics Theory (math.ST)
Cite as: arXiv:2210.02327 [math.AP]
  (or arXiv:2210.02327v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2210.02327

Submission history

From: Mirko D'Ovidio [view email]
[v1] Wed, 5 Oct 2022 15:26:45 UTC (339 KB)
[v2] Thu, 27 Oct 2022 14:16:29 UTC (340 KB)
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