Upper bounds of nodal sets for Gevrey regular parabolic equations

TL;DR

This paper establishes an upper bound on the size of nodal sets for solutions to second order parabolic equations with Gevrey regular coefficients, aligning with known bounds for analytic coefficients.

Contribution

It provides the first upper bound estimates for nodal sets in parabolic equations with Gevrey regularity, extending results known for analytic coefficients.

Findings

Upper bounds depend on time and match sharp bounds for analytic coefficients

Extends nodal set estimates to Gevrey regular coefficients

Bridges gap between analytic and less regular coefficient cases

Abstract

We consider the size of the nodal set of the solution of the second order parabolic-type equation with Gevrey regular coefficients. We provide an upper bound as a function of time. The dependence agrees with a sharp upper bound when the coefficients are analytic.