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Moderate deviation for random elliptic PDE with small noise. (English) Zbl 1402.60032

Summary: Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from imprecise measurement and intrinsic randomness. In this paper, we perform asymptotic rare-event analysis for such elliptic PDEs with random inputs. In particular, we consider the asymptotic regime that the noise level converges to zero suggesting that the system uncertainty is low, but does exist. We develop sharp approximations of the probability of a large class of rare events.

MSC:

60F10 Large deviations
60G15 Gaussian processes
35R60 PDEs with randomness, stochastic partial differential equations
35J25 Boundary value problems for second-order elliptic equations
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