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

2025/07/25 by Guoming Zhang, Zhang, Guoming
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2507.18898

openalex publication_date 2025/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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\mathringarding inequality) and time-independent coefficients. We also obtain Gaussian upper bounds and Hölder regularity estimates for the fundamental solutions of this class of parabolic equations.

Citations

• On fundamental solutions and Gaussian bounds for degenerate parabolic equations with time-dependent coefficients
• A universal variational framework for parabolic equations and systems
• Dirichlet and Neumann boundary values of solutions to higher order elliptic equations
• L² Solvability of boundary value problems for divergence form\n parabolic equations with complex coefficients
• Square function estimates on layer potentials for higher-order elliptic\n equations
• Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients
• Gaussian heat kernel bounds through elliptic Moser iteration
• A new proof of Moser's parabolic harnack inequality using the old ideas of Nash

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• Gaussian lower bounds for non-homogeneous Kolmogorov equations with\n measurable coefficients