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Transmission problems: regularity theory, interfaces and beyond

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arxiv 2306.15570 v1 pith:PMK2H34Y submitted 2023-06-27 math.AP

Vincenzo Bianca , Edgard A. Pimentel , José Miguel Urbano This is my paper
classification math.AP
keywords problemsregularitytransmissioninterfacesdiscussiontheoryacrossaddressing
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Modelling diffusion processes in heterogeneous media requires addressing inherent discontinuities across interfaces, where specific conditions are to be met. These challenges fall under the purview of Mathematical Analysis as \emph{transmission problems}. We present a pa\-no\-ra\-ma of the theory of transmission problems, encompassing the seminal contributions from the 1950s and subsequent developments. Then we delve into the discussion of regularity issues, including recent advances matching the minimal regularity requirements of interfaces and the optimal regularity of the solutions. A discussion on free transmission problems closes the survey.

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Cited by 1 Pith paper

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  1. Numerical methods for fully nonlinear degenerate diffusions

    math.NA 2025-06 reject novelty 4.0 of 10

    The paper claims convergent finite difference schemes for degenerate fully nonlinear diffusions, but the displayed schemes do not approximate the target equations and the monotonicity proof fails.

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