On the one-dimensional parabolic obstacle problem with variable coefficients

Mathematics – Analysis of PDEs

Scientific paper

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bcd-note

Scientific paper

This note is devoted to continuity results of the time derivative of the
solution to the one-dimensional parabolic obstacle problem with variable
coefficients. It applies to the smooth fit principle in numerical analysis and
in financial mathematics. It relies on various tools for the study of free
boundary problems: blow-up method, monotonicity formulae, Liouville's results.

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