Dimensional Universality of Schauder Estimates Constants for Fourth Order Heat-Type Equations

A new method to compute Schauder Estimates for multidimensional fourth order heat-type equations is proposed. In particular, we show how knowing Schauder or Sobolev estimates for the one-dimensional fourth order heat equation allows to derive their multidimensional analogs for equations with time in...

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Bibliographic Details
Published in:arXiv.org 2022-09
Main Authors: Cangiotti, Nicolò, Marino, Lorenzo
Format: Article
Language:English
Subjects:
Estimates
Temperature
Thermodynamics
Online Access:Get full text
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Summary:A new method to compute Schauder Estimates for multidimensional fourth order heat-type equations is proposed. In particular, we show how knowing Schauder or Sobolev estimates for the one-dimensional fourth order heat equation allows to derive their multidimensional analogs for equations with time inhomogeneous coefficients with the same constants as in the case of the one-dimensional heat equation. Our method relies on a merger between (Krylov and Priola, 2017), where they actually showed the same result for the classical second order heat equation and (Funaki, 1979), where a probabilistic construction of solutions for the fourth order heat equation is presented.
ISSN:2331-8422