Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications

By Pierre-Louis Lions, Panagiotis E. Souganidis. 2005

110 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0faa63e0b2caf0f79efd98579f47f830da7775f2

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Asymptotic and numerical homogenization (2008, methodology): “The proof of the theorem in Lions and Souganidis (2005a) is based strongly on the (stochastic) control interpretation of (5.6), which is available due to the assumptions that H is convex and A independent of Du, and the use of the (sub-additive) ergodic theorem.”
Spreading speeds for one-dimensional monostable reaction-diffusion equations (2016, methodology): “To do so, we follow the ideas developed by Majda and Souganidis in [22], which are based on the half-limits method.”
Rates of convergence for the homogenization of fully nonlinear uniformly elliptic pde in random media (2010, background): “It is then follows (see [ 22 ]a nd [14] for such arguments) that, as e → 0, ue →¯ u where ¯ u is the solution of (1.2) with ¯”
Large Deviations and Importance Sampling for Systems of Slow-Fast Motion (2012, methodology): “We refer the interested reader to the literature of homogenization for Hamilton-Jacobi-Bellman equations for more detailed discussions, e.g. [1, 2, 9, 20, 25, 31].”
Hölder estimates for degenerate elliptic equations with coercive Hamiltonians (2010, background): “Anyway, this approach requires the coercivity of the Hamiltonian (a somehow necessary ingredient for having estimates in the case of degenerate ellipticity; see also [14]).”
Nonlinear elliptic systems and mean-field games (2016, methodology): “The proof of the existence of solutions to (1) under condition C1 follows the suggestion in [44, 46] about getting a priori estimates for Dvi by the Bernstein method (see also [1], [47] and [48]).”
Homogenization of “Viscous” Hamilton–Jacobi Equations in Stationary Ergodic Media (2005, methodology): “[ LS2 ], always in the almost periodic setting, to nonlinear versions (1.1) and (1.7).”