Poisson stochastic process and basic Schauder and Sobolev estimates in the theory of parabolic equations
Analysis of PDEs
2017-06-07 v3
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 {\em 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.
Keywords
Cite
@article{arxiv.1607.00957,
title = {Poisson stochastic process and basic Schauder and Sobolev estimates in the theory of parabolic equations},
author = {N. V. Krylov and E. Priola},
journal= {arXiv preprint arXiv:1607.00957},
year = {2017}
}
Comments
37 pages, more discussion and references added, some errors corrected