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arXiv · 2607.02979

A two-dimensional structural local-defect theory for scalar non-divergence advection-diffusion homogenization

Jizu Huang·Yong Ma
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Abstract

We develop a two-dimensional structural local-defect theory for scalar non-divergence advection--diffusion operators \(Lu=-a:D^2u+b\cdot\nabla u\), where \(a=a^{\mathrm{per}}+a^e\) and \(b=b^{\mathrm{per}}+b^e\). The periodic coefficients and the bounded local defects are uniformly H\"older continuous, the interpolating matrices \(a_t=a^{\mathrm{per}}+t a^e\) are symmetric and uniformly elliptic, and \(a^e\in L^r(\mathbb{R}^2)\), \(b^e\in L^s(\mathbb{R}^2)\), where \(1 0\), the defects \(B^e\) and \(A^e:=ma-B-(m^{\mathrm{per}}a^{\mathrm{per}}-B^{\mathrm{per}})\) belong to \(L^{M^*}\cap L^\infty\cap C_{\mathrm{unif}}^{0,\beta}\) and vanish uniformly at infinity. This supplies the missing two-dimensional structural reduction in the scalar regular non-endpoint regime.

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Jizu Huang, Yong Ma. 2026-07-03. A two-dimensional structural local-defect theory for scalar non-divergence advection-diffusion homogenization. https://arxiv.org/abs/2607.02979

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