Homogenization of diffusion processes with singular drifts and potentials via unfolding method

2023/06/25 by Uemura, Toshihiro, Seesanea, Adisak
#31C25 (Primary) 60J46 #35B27 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2306.14307

Abstract

This work is concerned with homogenization problems for elliptic equations of the type \begincases \mathfrakL_δ u_δ + λu_δ = f_δ in D,
u = 0 on ∂ D, \endcases where δ> 0, λ∈ ℝ, D is a bounded open set in ℝ^d, and f_δ ∈ H^-1(D). The operator \mathfrakL_δ u = -\rm div ( A^δ∇ u + C^δu ) + B^δ∇ u +k^δu involved uniformly bounded diffusion coefficients A^δ, where drifts B^δ, C^δ, and potential k^δ are possibly unbounded. An application to homogenization of the corresponding diffusion processes is also discussed.

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