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Subsolutions That Are Close in the Uniform Norm Are Close in the Sobolev Norm as Well

Subsolutions That Are Close in the Uniform Norm Are Close in the Sobolev Norm as Well A new type weighted reverse Poincaré inequality is established for a difference of two continuous weak subsolutions of a linear second order uniformly elliptic partial differential equation in the ball. This result is the key to deriving the error estimate for the gradient of the analytically unknown value function of the optimal stochastic control problem from the uniform error of the value function itself in the related numerical approximation problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Subsolutions That Are Close in the Uniform Norm Are Close in the Sobolev Norm as Well

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References (26)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Science+Business Media, LLC
Subject
Mathematics; Mathematical Methods in Physics; Calculus of Variations and Optimal Control; Optimization; Numerical and Computational Physics; Theoretical, Mathematical and Computational Physics; Systems Theory, Control
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-012-9161-5
Publisher site
See Article on Publisher Site

Abstract

A new type weighted reverse Poincaré inequality is established for a difference of two continuous weak subsolutions of a linear second order uniformly elliptic partial differential equation in the ball. This result is the key to deriving the error estimate for the gradient of the analytically unknown value function of the optimal stochastic control problem from the uniform error of the value function itself in the related numerical approximation problems.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Aug 1, 2012

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