Gaussian estimates for fundamental solutions of higher-order parabolic equations with time-independent coefficients

Guoming Zhang

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arXiv · 2507.18898

Gaussian estimates for fundamental solutions of higher-order parabolic equations with time-independent coefficients

Guoming Zhang

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Abstract

We study the De Giorgi-Moser-Nash estimates of higher-order parabolic equations in divergence form with complex-valued, measurable, bounded, uniformly elliptic (in the sense of G$\mathring{a}$rding inequality) and time-independent coefficients. We also obtain Gaussian upper bounds and H\"{o}lder regularity estimates for the fundamental solutions of this class of parabolic equations.

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Guoming Zhang. 2025-07-25. Gaussian estimates for fundamental solutions of higher-order parabolic equations with time-independent coefficients. https://arxiv.org/abs/2507.18898

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