Degenerate parabolic equations in divergence form: fundamental solution and Gaussian bounds

期刊论文
出版模式：

开放获取
发表日期：

2026年3月31日

查看全文

Khalid Baadi

摘要

In this paper, we consider second-order degenerate parabolic equations with complex, measurable, and time-dependent coefficients. The degenerate ellipticity is dictated by a spatial $A_2$ $A_{2}$ -weight. We prove that having a generalized fundamental solution with upper Gaussian bounds is equivalent to Moser’s $L^2$ $L^{2}$ - $L^\infty $ $L^{\infty}$ estimates for local weak solutions. In the special case of real coefficients, Moser’s $L^2$ $L^{2}$ - $L^\infty $ $L^{\infty}$ estimates are known, which provide an easier proof of Gaussian upper bounds, and a known Harnack inequality is then used to derive Gaussian lower bounds.