4 citations · 5 across the 7 of their papers we have counts for
9 papers
A starlike 3-dimensional counterexample to the hot spots conjecture
Rami Atar, Krzysztof Burdzy
We construct a bounded Lipschitz domain in that is starlike about the origin and whose first positive Neumann eigenvalue is simple. A corresponding eigenfunction, af…
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…
Geometric properties of optimizers for the maximum gradient of the torsion function
Krzysztof Burdzy, Ilias Ftouhi, Phanuel Mariano
Consider and , where is a planar convex domain, is the torsion function, is the pe…
Uniqueness for the Skorokhod problem in an orthant: critical cases
Richard F. Bass, Krzysztof Burdzy
Consider the Skorokhod problem in the closed non-negative orthant: find a solution to \[ g(t)= f(t)+ Rm(t),\] where is a given continuous vector-valued function w…
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…
Pathwise non-uniqueness for Brownian motion in a quadrant with oblique reflection
Richard F. Bass, Krzysztof Burdzy
Consider the Skorokhod equation in the closed first quadrant: \[ X_t=x_0+ B_t+\int_0^t{\bf v}(X_s)\, dL_s,\] where is standard 2-dimensional Brownian motion, takes valu…
Pinned Billiard Balls Simulation (WXML Autumn 2023 report)
Bella Cochran, Anish Gupta, Colin Holzman-Klima +3
Systems of pinned billiard balls serve as simplified models of collisions, where all particles remain fixed in their positions while their (pseudo-)velocities evolve in accordance…
Non-uniqueness for non-negative solutions of parabolic stochastic partial differential equations
K. Burdzy, C. Mueller, E. A. Perkins
Pathwise non-uniqueness is established for non-negative solutions of the parabolic stochastic pde where $\dot…
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…