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 time variable with the same\ constants as in the case of the one-dimensional heat equation. The method is based on using the Poisson stochastic process. It looks like no other method is available at this time and it is a very challenging problem to find a purely analytic approach to proving such results.

Poisson stochastic process and basic Schauder and Sobolev estimates in the theory of parabolic equations

PRIOLA, Enrico
2017-01-01

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 time variable with the same\ constants as in the case of the one-dimensional heat equation. The method is based on using the Poisson stochastic process. It looks like no other method is available at this time and it is a very challenging problem to find a purely analytic approach to proving such results.
2017
225
3
1089
1126
https://arxiv.org/abs/1607.00957
Schauder estimates, Poisson process
Krylov, N.V.; Priola, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1621831
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