Weighted Parabolic Aleksandrov Estimates: PDE and Stochastic Versions

N. V. Krylov

doi:10.1007/s10958-019-04627-w

Weighted Parabolic Aleksandrov Estimates: PDE and Stochastic Versions

N. V. Krylov

School of Mathematics

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

Abstract

We prove several pointwise estimates for solutions of linear parabolic equations with measurable coefficients in smooth cylinders through the weighted L_d+1-norm of the free term. The weights allow the free term to blow up near the lateral boundary. These are the first such results for parabolic equations with measurable coefficients. We also present the corresponding weighted estimates for occupation times of diffusion processes.

Original language	English (US)
Pages (from-to)	419-435
Number of pages	17
Journal	Journal of Mathematical Sciences (United States)
Volume	244
Issue number	3
DOIs	https://doi.org/10.1007/s10958-019-04627-w
State	Published - Jan 1 2020

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abstract = "We prove several pointwise estimates for solutions of linear parabolic equations with measurable coefficients in smooth cylinders through the weighted Ld+1-norm of the free term. The weights allow the free term to blow up near the lateral boundary. These are the first such results for parabolic equations with measurable coefficients. We also present the corresponding weighted estimates for occupation times of diffusion processes.",

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AB - We prove several pointwise estimates for solutions of linear parabolic equations with measurable coefficients in smooth cylinders through the weighted Ld+1-norm of the free term. The weights allow the free term to blow up near the lateral boundary. These are the first such results for parabolic equations with measurable coefficients. We also present the corresponding weighted estimates for occupation times of diffusion processes.

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Weighted Parabolic Aleksandrov Estimates: PDE and Stochastic Versions

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