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In this paper, we consider a family of second-order elliptic systems subject to a periodically oscillating Robin boundary condition. We establish the qualitative homogenization theorem on any Lipschitz domains satisfying a non-resonance condition. We also use the quantitative estimates of oscillatory integrals to obtain the dimension-dependent convergence rates in $L^2$, assuming that the domain is smooth and strictly convex.
This paper is concerned with boundary regularity estimates in the homogenization of elliptic equations with rapidly oscillating and high-contrast coefficients. We establish uniform nontangential-maximal-function estimates for the Dirichlet, regularit
In many cases, groundwater flow in an unconfined aquifer can be simplified to a one-dimensional Sturm-Liouville model of the form: begin{equation*} x(t)+lambda x(t)=h(t)+varepsilon f(x(t)),hspace{.1in}tin(0,pi) end{equation*} subject to non-local bou
We consider elliptic equations and systems in divergence form with the conormal or the Robin boundary conditions, with small BMO (bounded mean oscillation) or variably partially small BMO coefficients. We propose a new class of domains which are loca
We study the large time behaviour of the solution of linear dispersive partial differential equations posed on a finite interval, when at least one of the prescribed boundary conditions is time periodic. We use the Q equation approach, pioneered in F
We study homogenization of a boundary obstacle problem on $ C^{1,alpha} $ domain $D$ for some elliptic equations with uniformly elliptic coefficient matrices $gamma$. For any $ epsiloninmathbb{R}_+$, $partial D=Gamma cup Sigma$, $Gamma cap Sigma=empt