Two-sided Gaussian bounds for fundamental solutions of non-divergence form parabolic operators with H\"older continuous coefficients

TL;DR

This paper derives two-sided Gaussian bounds for fundamental solutions of non-divergence form parabolic operators with H"older continuous coefficients, using the parametrix method, advancing understanding of their behavior.

Contribution

It provides new two-sided Gaussian bounds for fundamental solutions of such operators, based on the parametrix method, with less regular coefficients than previously handled.

Findings

Established two-sided Gaussian bounds for fundamental solutions.

Applied parametrix method to operators with H"older continuous coefficients.

Enhanced theoretical understanding of parabolic operators with irregular coefficients.

Abstract

We establish two-sided Gaussian bounds for fundamental solutions of general non-divergence form parabolic operators with H\"older continuous coefficients. The result we obtain is essentially based on parametrix method.