ALERT: This system is being upgraded on Tuesday December 12. It will not be available for use for several hours that day while the upgrade is in progress. Deposits to DukeSpace will be disabled on Monday December 11, so no new items are to be added to the repository while the upgrade is in progress. Everything should be back to normal by the end of day, December 12.

Browsing by Author "Steinerberger, Stefan"

Now showing items 1-3 of 3

    • A Variation on the Donsker-Varadhan Inequality for the Principial Eigenvalue 

      Lu, Jianfeng; Steinerberger, Stefan (2017-04-23)
      The purpose of this short note is to give a variation on the classical Donsker-Varadhan inequality, which bounds the first eigenvalue of a second-order elliptic operator on a bounded domain $\Omega$ by the largest mean first ...

    • Non-Convex Planar Harmonic Maps 

      Kovalsky, Shahar Z; Aigerman, Noam; Daubechies, Ingrid; Kazhdan, Michael; Lu, Jianfeng; Steinerberger, Stefan
      We formulate a novel characterization of a family of invertible maps between two-dimensional domains. Our work follows two classic results: The Rad\'o-Kneser-Choquet (RKC) theorem, which establishes the invertibility of harmonic ...

    • Riesz Energy on the Torus: Regularity of Minimizers 

      Lu, Jianfeng; Steinerberger, Stefan (2017-11-30)
      We study sets of $N$ points on the $d-$dimensional torus $\mathbb{T}^d$ minimizing interaction functionals of the type \[ \sum_{i, j =1 \atop i \neq j}^{N}{ f(x_i - x_j)}. \] The main result states that for a class of functions ...