Poisson stochastic process and basic schauder and Sobolev estimates in the theory of parabolic equations (short version)

N. V. Krylov; E. Priola

doi:10.1007/978-3-319-74929-7_10

Poisson stochastic process and basic schauder and Sobolev estimates in the theory of parabolic equations (short version)

N. V. Krylov, E. Priola

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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 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 method is available at this time and it is a very challenging problem to find a purely analytic approach to proving such results. We only give examples of applications of our results. Their proofs will appear elsewhere.

Original language	English (US)
Title of host publication	Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016
Editors	Gerald Trutnau, Andreas Eberle, Walter Hoh, Moritz Kassmann, Martin Grothaus, Wilhelm Stannat
Publisher	Springer New York LLC
Pages	201-211
Number of pages	11
ISBN (Print)	9783319749280
DOIs	https://doi.org/10.1007/978-3-319-74929-7_10
State	Published - 2018
Event	International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016 - Bielefeld, Germany Duration: Oct 10 2016 → Oct 14 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	229
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Other

Other	International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016
Country/Territory	Germany
City	Bielefeld
Period	10/10/16 → 10/14/16

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

Keywords

Multidimensional parabolic equations
Poisson process
Schauder estimates
Sobolev-space estimates

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10.1007/978-3-319-74929-7_10

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Krylov, N. V., & Priola, E. (2018). Poisson stochastic process and basic schauder and Sobolev estimates in the theory of parabolic equations (short version). In G. Trutnau, A. Eberle, W. Hoh, M. Kassmann, M. Grothaus, & W. Stannat (Eds.), Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016 (pp. 201-211). (Springer Proceedings in Mathematics and Statistics; Vol. 229). Springer New York LLC. https://doi.org/10.1007/978-3-319-74929-7_10

Poisson stochastic process and basic schauder and Sobolev estimates in the theory of parabolic equations (short version). / Krylov, N. V.; Priola, E.
Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. ed. / Gerald Trutnau; Andreas Eberle; Walter Hoh; Moritz Kassmann; Martin Grothaus; Wilhelm Stannat. Springer New York LLC, 2018. p. 201-211 (Springer Proceedings in Mathematics and Statistics; Vol. 229).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Krylov, NV & Priola, E 2018, Poisson stochastic process and basic schauder and Sobolev estimates in the theory of parabolic equations (short version). in G Trutnau, A Eberle, W Hoh, M Kassmann, M Grothaus & W Stannat (eds), Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. Springer Proceedings in Mathematics and Statistics, vol. 229, Springer New York LLC, pp. 201-211, International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016, Bielefeld, Germany, 10/10/16. https://doi.org/10.1007/978-3-319-74929-7_10

Krylov NV, Priola E. Poisson stochastic process and basic schauder and Sobolev estimates in the theory of parabolic equations (short version). In Trutnau G, Eberle A, Hoh W, Kassmann M, Grothaus M, Stannat W, editors, Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. Springer New York LLC. 2018. p. 201-211. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-319-74929-7_10

Krylov, N. V. ; Priola, E. / Poisson stochastic process and basic schauder and Sobolev estimates in the theory of parabolic equations (short version). Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. editor / Gerald Trutnau ; Andreas Eberle ; Walter Hoh ; Moritz Kassmann ; Martin Grothaus ; Wilhelm Stannat. Springer New York LLC, 2018. pp. 201-211 (Springer Proceedings in Mathematics and Statistics).

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Poisson stochastic process and basic schauder and Sobolev estimates in the theory of parabolic equations (short version)

Abstract

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Keywords

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