Direct methods in the theory of elliptic equations

By J. Necas, Š. Nečasová, Christian Simader. 2012

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On large deviations of coupled diffusions with time scale separation (2013, background): “f S2 is a ball containing S1, then, for some c>0, kws(u,·)k2 W1,2(S2) ≤ c(kDws(u,·)k 2 L2(S2) + kws(u,·)k2 L2(S1) ), see p.299 in Kufner, John, and Fuˆcik [26], also Theorem 7.4 on p.109 in Neˇcas [31]. Thus, Zt 0 sup u:|u|≤L kws(u,·)k2 W1,2(S2) ds<∞. (7.27) Let S˘ represent an open ball in Rl”
The Heston Stochastic-Local Volatility Model: Efficient Monte Carlo Simulation (2014, neutral): “where α is some positive constant, related to the V−ellipticity of the form ∫ Ω eL1edΩ [17].”