C 1+α-Regularity of Viscosity Solutions of General Nonlinear Parabolic Equations

N. V. Krylov

doi:10.1007/s10958-018-3880-3

C ^1+α-Regularity of Viscosity Solutions of General Nonlinear Parabolic Equations

N. V. Krylov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We establish the existence of C^1+α-regular viscosity solutions of fully nonlinear secondorder parabolic equations like ∂_tu+H(v,Dv,D²v, t, x) = 0 allowing the main part of H to have small discontinuities with respect to x and be just measurable in t.

Original language	English (US)
Pages (from-to)	403-427
Number of pages	25
Journal	Journal of Mathematical Sciences (United States)
Volume	232
Issue number	4
DOIs	https://doi.org/10.1007/s10958-018-3880-3
State	Published - Jul 1 2018

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Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

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10.1007/s10958-018-3880-3

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abstract = "We establish the existence of C1+α-regular viscosity solutions of fully nonlinear secondorder parabolic equations like ∂tu+H(v,Dv,D2v, t, x) = 0 allowing the main part of H to have small discontinuities with respect to x and be just measurable in t.",

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AB - We establish the existence of C1+α-regular viscosity solutions of fully nonlinear secondorder parabolic equations like ∂tu+H(v,Dv,D2v, t, x) = 0 allowing the main part of H to have small discontinuities with respect to x and be just measurable in t.

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