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arXiv · 1610.08064

Fundamental matrices and Green matrices for non-homogeneous elliptic systems

Blair Davey·Jonathan Hill·Svitlana Mayboroda
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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 $\mathbb{R}^n$ 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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Blair Davey, Jonathan Hill, Svitlana Mayboroda. 2016-10-25. Fundamental matrices and Green matrices for non-homogeneous elliptic systems. https://arxiv.org/abs/1610.08064

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