Poisson Stochastic Process and Basic Schauder and Sobolev Estimates in the Theory of Parabolic Equations

N. V. Krylov, E. Priola

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We show, among other things, how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on the time variable with the same constants as in the case of the one-dimensional heat equation. The method is quite general and is based on using the Poisson stochastic process. It also applies to equations involving non-local operators. It looks like no other methods are available at this time and it is a very challenging problem to find a purely analytical approach to proving such results.

Original languageEnglish (US)
Pages (from-to)1089-1126
Number of pages38
JournalArchive For Rational Mechanics And Analysis
Volume225
Issue number3
DOIs
StatePublished - Sep 1 2017

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