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.
Transmission problems: regularity theory, interfaces and beyond
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abstract
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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Numerical methods for fully nonlinear degenerate diffusions
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.