TY - JOUR
T1 - Stochastic homogenization of L ∞ variational problems
AU - Armstrong, Scott N.
AU - Souganidis, Panagiotis E.
N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (S.N. Armstrong), [email protected] (P.E. Souganidis). 1 Partially supported by NSF Grant DMS-1004645. 2 Partially supported by NSF Grant DMS-0901802.
Funding Information:
The first author was partially supported by NSF Grant DMS-1004645 and the second author by NSF Grant DMS-0901802. The first author also thanks Charlie Smart and Vesa Julin for helpful conversations. We acknowledge an anonymous referee for suggesting the example at the end of Section 5.
PY - 2012/4/1
Y1 - 2012/4/1
N2 - We present a homogenization result for L ∞ variational problems in general stationary ergodic random environments. By introducing a generalized notion of distance function (a special solution of an associated eikonal equation) and demonstrating a connection to absolute minimizers of the variational problem, we obtain the homogenization result as a consequence of the fact that the latter homogenizes in random environments.
AB - We present a homogenization result for L ∞ variational problems in general stationary ergodic random environments. By introducing a generalized notion of distance function (a special solution of an associated eikonal equation) and demonstrating a connection to absolute minimizers of the variational problem, we obtain the homogenization result as a consequence of the fact that the latter homogenizes in random environments.
KW - Eikonal equation
KW - Hamilton-Jacobi equation
KW - L calculus of variations
KW - Stochastic homogenization
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U2 - 10.1016/j.aim.2012.02.018
DO - 10.1016/j.aim.2012.02.018
M3 - Article
AN - SCOPUS:84857580800
SN - 0001-8708
VL - 229
SP - 3508
EP - 3535
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 6
ER -