Fundamental matrices and Green matrices for non-homogeneous elliptic systems

2016/10/25 by Davey, Blair, Hill, Jonathan, Mayboroda, Svitlana
#35A08 #35B45 #35J08 #35J10 #35J57 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.08064

Abstract

In this paper, we establish existence, uniqueness, and scale-invariant estimates for fundamental solutions of non-homogeneous second order elliptic systems with bounded measurable coefficients in ℝⁿ and for the corresponding Green functions in arbitrary open sets. We impose certain non-homogeneous versions of de Giorgi-Nash-Moser bounds on the weak solutions and investigate in detail the assumptions on the lower order terms sufficient to guarantee such conditions.

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