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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Weighted Aleksandrov estimates: PDE and stochastic versions


Author: N. V. Krylov
Original publication: Algebra i Analiz, tom 31 (2019), nomer 3.
Journal: St. Petersburg Math. J. 31 (2020), 509-520
MSC (2010): Primary 35J15, 35J60, 60H05
DOI: https://doi.org/10.1090/spmj/1611
Published electronically: April 30, 2020
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Abstract | References | Similar Articles | Additional Information

Abstract: Several pointwise estimates are proved for solutions of linear elliptic equations with measurable coefficients in smooth domains through the weighted $ L_d$-norm of the free term. The weights allow the free term to blow up near the boundary. Weighted estimates for occupation times of diffusion processes are also presented.


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Additional Information

N. V. Krylov
Affiliation: University of Minnesota, 127 Vincent Hall, Minneapolis, MN, 55455
Email: nkrylov@umn.edu

DOI: https://doi.org/10.1090/spmj/1611
Keywords: Weights, Aleksandrov estimates, elliptic equations
Received by editor(s): September 24, 2018
Published electronically: April 30, 2020
Dedicated: In memory of S. G. Mikhlin
Article copyright: © Copyright 2020 American Mathematical Society