Stochastic Homogenization of Hamilton-Jacobi Equations in Stationary Ergodic Spatio-Temporal Media

Stochastic Homogenization of Hamilton-Jacobi Equations in Stationary Ergodic Spatio-Temporal Media

This paper considers the problem of homogenization of a class of convex Hamilton-Jacobi equations in spatio-temporal stationary ergodic environments. Special attention is placed on the interplay between the use of the Subadditive Ergodic Theorem and continuity estimates for the solutions that are in...

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Veröffentlicht in:Indiana University mathematics journal 2009-01, Vol.58 (2), p.537-581
1. Verfasser: Schwab, Russell W.
Format: Artikel
Sprache:eng
Schlagworte:
Applications
Biology, psychology, social sciences
Convexity
Ergodic theory
Exact sciences and technology
General mathematics
General, history and biography
Hamilton Jacobi equation
Homogenization
Mathematical analysis
Mathematical functions
Mathematics
Partial differential equations
Perceptron convergence procedure
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Stochastic analysis
Time dependence
Uniqueness
Viscosity
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Beschreibung
Zusammenfassung:This paper considers the problem of homogenization of a class of convex Hamilton-Jacobi equations in spatio-temporal stationary ergodic environments. Special attention is placed on the interplay between the use of the Subadditive Ergodic Theorem and continuity estimates for the solutions that are independent of the oscillations in the equation. Moreover, an inf-sup formula for the effective Hamiltonian is provided.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2009.58.3455