Krzysztof Burdzy

activity

20022026

most citedNon-uniqueness for non-negative solutions of parabolic stochastic partial differential equations

4 citations · 5 across the 7 of their papers we have counts for

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5 papers · 1 filter

math.AP2026

A starlike 3-dimensional counterexample to the hot spots conjecture

Rami Atar, Krzysztof Burdzy

We construct a bounded Lipschitz domain in $R^{3}$ that is starlike about the origin and whose first positive Neumann eigenvalue is simple. A corresponding eigenfunction, af…

math.AP2026

Removing Boundary Smoothness from the Hot-Spots Conclusion in the Simple-Eigenvalue Case

Krzysztof Burdzy

We give a reduction from a smooth-domain theorem excluding interior critical points of first positive Neumann eigenfunctions to a non-strict hot-spots conclusion on arbitrary bound…

math.AP2025

Geometric properties of optimizers for the maximum gradient of the torsion function

Krzysztof Burdzy, Ilias Ftouhi, Phanuel Mariano

Consider $J (Ω) := ∥\nabla u_{Ω} ∥_{\infty} / ∣Ω∣$ and $J_{P} (Ω) := ∥\nabla u_{Ω} ∥_{\infty} / P (Ω)$ , where $Ω$ is a planar convex domain, $u_{Ω}$ is the torsion function, $P (Ω)$ is the pe…

math.AP2024

Coupled transport equations with freezing

Krzysztof Burdzy, John Sylvester

We study a system of two coupled transport equations with freezing. The solutions freeze in time when they are equal. We prove existence and uniqueness of continuous solutions if t…

math.AP2002

On nodal lines of Neumann eigenfunctions

Krzysztof Burdzy

We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain. The technique is based on the `mirror coupling' of refle…