359 citations · 1k across the 39 of their papers we have counts for
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Quantitative analysis of boundary layers in periodic homogenization
Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat +1
We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estim…
Equivalence of solutions to fractional -Laplace type equations
Janne Korvenpää, Tuomo Kuusi, Erik Lindgren
In this paper, we study different notions of solutions of nonlocal and nonlinear equations of fractional -Laplace type $${\rm P.V.} \int_{\mathbb R^n}\frac{|u(x)-u(y)|^{p-2}(u(x…
Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations
Janne Korvenpaa, Tuomo Kuusi, Giampiero Palatucci
We deal with a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order and summability growth , whos…
The obstacle problem for nonlinear integro-differential operators
Janne Korvenpaa, Tuomo Kuusi, Giampiero Palatucci
We investigate the obstacle problem for a class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional -La…
Scaling limits of energies and correctors
Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
In stochastic homogenization of elliptic equations, the corrector plays a central role. Under a finite range of dependence assumption on the coefficient field, we show that the lar…
The additive structure of elliptic homogenization
Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
One of the principal difficulties in stochastic homogenization is transferring quantitative ergodic information from the coefficients to the solutions, since the latter are nonloca…