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Mathematics of Computation

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First derivatives estimates for finite-difference schemes


Authors: István Gyöngy and Nicolai Krylov
Journal: Math. Comp. 78 (2009), 2019-2046
MSC (2000): Primary 65M06, 39A70
DOI: https://doi.org/10.1090/S0025-5718-09-02229-7
Published electronically: February 11, 2009
MathSciNet review: 2521277
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Abstract: We give sufficient conditions under which solutions of discretized in space second-order parabolic and elliptic equations, perhaps degenerate, admit estimates of the first derivatives in the space variables independent of the mesh size.


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Additional Information

István Gyöngy
Affiliation: School of Mathematics, University of Edinburgh, King’s Buildings, Edinburgh, EH9 3JZ, United Kingdom
Email: gyongy@maths.ed.ac.uk

Nicolai Krylov
Affiliation: 127 Vincent Hall, University of Minnesota, Minneapolis, Minnesota, 55455
Email: krylov@math.umn.edu

DOI: https://doi.org/10.1090/S0025-5718-09-02229-7
Keywords: Cauchy problem, finite differences, first derivatives estimates
Received by editor(s): January 22, 2008
Received by editor(s) in revised form: September 26, 2008
Published electronically: February 11, 2009
Additional Notes: The work of the second author was partially supported by NSF grant DMS-0653121
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.