On the random G equation with nonzero divergence

We prove a quantitative rate of homogenization for the G equation in a random setting with finite range of dependence and nonzero divergence, with explicit dependence of the constants on the Lipschitz norm of the environment. Inspired by work of Burago–Ivanov–Novikov, the proof uses explicit bounds...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2023-09, Vol.62 (7), Article 211
Main Author: Cooperman, William
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
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Summary:We prove a quantitative rate of homogenization for the G equation in a random setting with finite range of dependence and nonzero divergence, with explicit dependence of the constants on the Lipschitz norm of the environment. Inspired by work of Burago–Ivanov–Novikov, the proof uses explicit bounds on the waiting time for the associated metric problem.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-023-02555-x