Cory J. Wright, Ph.D.

Ph.D.

Mathematics

University of Nebraska at Lincoln

2018

M.S.

Mathematics

University of Nebraska at Lincoln

2015

B.S.

Mathematics

Rowan University

2013

Minor in Physics & Astronomy

MCTP Graduate Fellowship

University of Nebraska at Lincoln 2013-2014

Nonlocal Trace Theorems and Their Applications

SIAM Central States Annual Meeting  

2019-10-19

"Existence and Regularity of Minimizers for Nonlocal Energy Functionals"

Spring Southeast Sectional Meeting of the AMS, Analysis Control and Stabilization of PDE's Session  College of Charleston, Charleston, SC

2017-03-10

Nonlocal Trace Spaces and Extension Results for Nonlocal Calculus

For a given Lipschitz domain Ω, it is a classical result that the trace space of W1,p(Ω) is W1−1/p,p(∂Ω), namely any W1,p(Ω) function has a well-defined W1−1/p,p(∂Ω) trace on its codimension-1 boundary ∂Ω and any W1−1/p,p(∂Ω) function on ∂Ω can be extended to a W1,p(Ω) function. Recently, Dyda and Kassmann (2019) characterize the trace space for nonlocal Dirichlet problems involving integrodifferential operators with infinite interaction ranges, where the boundary datum is provided on the whole complement of the given domain ℝd∖Ω.

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Existence and regularity of minimizers for nonlocal energy functionals

In this paper, we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics [19] or nonlocal diffusion models [1]. We derive nonlocal versions of the Euler-Lagrange equations under two sets of growth assumptions for the integrand. Existence of minimizers is shown for integrands with joint convexity (in the function and nonlocal gradient components). By using the convolution structure, we show regularity of solutions for certain Euler-Lagrange equations.

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Four derivations of an interesting bilateral series generalizing the series for zeta of 2

We present four derivations of the closed form of the partial fractions expansion


This interesting series is a generalization of the series made famous by Euler.

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