Upper bounds of nodal sets for Gevrey regular parabolic equations

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.

💡 Research Summary

The paper investigates quantitative upper bounds for the (d‑1)-dimensional Hausdorff measure of the nodal (zero) set of solutions to a second‑order parabolic equation with Gevrey‑regular coefficients. The model problem is
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