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• W3098364106 abstract "The aim of this article is to show how certain parabolic theorems follow from their elliptic counterparts. This technique is demonstrated through new proofs of five important theorems in parabolic unique continuation and the regularity theory of parabolic equations and geometric flows. Specifically, we give new proofs of an $L^2$ Carleman estimate for the heat operator, and the monotonicity formulas for the frequency function associated to the heat operator, the two-phase free boundary problem, the flow of harmonic maps, and the mean curvature flow. The proofs rely only on the underlying elliptic theorems and limiting procedures belonging essentially to probability theory. In particular, each parabolic theorem is proved by taking a high-dimensional limit of the related elliptic result." @default.
• W3098364106 created "2020-11-23" @default.
• W3098364106 creator A5070657384 @default.
• W3098364106 date "2017-10-31" @default.
• W3098364106 modified "2023-09-26" @default.
• W3098364106 title "Parabolic Theory as a High-Dimensional Limit of Elliptic Theory" @default.
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• W3098364106 doi "https://doi.org/10.1007/s00205-017-1187-z" @default.
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