109 citations · 522 across the 51 of their papers we have counts for
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A partial differential equation for the strictly quasiconvex envelope
Bilal Abbasi, Adam M. Oberman
In a series of papers Barron, Goebel, and Jensen studied Partial Differential Equations (PDE)s for quasiconvex (QC) functions \cite{barron2012functions, barron2012quasiconvex,barro…
Computing the quasiconvex envelope using a nonlocal line solver
Bilal Abbasi, Adam M. Oberman
Recently in a series of articles, Barron, Goebel, and Jensen \cite{barron2012functions} \cite{barron2012quasiconvex} \cite{barron2013quasiconvex} \cite{barron2013uniqueness} have s…
Finite difference methods for fractional Laplacians
Yanghong Huang, Adam Oberman
The fractional Laplacian is the prototypical non-local elliptic operator. While analytical theory has been advanced and understood for some time, there remain many ope…
Numerical methods for motion of level sets by affine curvature
Adam M. Oberman, Tiago Salvador
We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference scheme…
Anomaly detection and classification for streaming data using PDEs
Bilal Abbasi, Jeff Calder, Adam M. Oberman
Nondominated sorting, also called Pareto Depth Analysis (PDA), is widely used in multi-objective optimization and has recently found important applications in multi-criteria anomal…
A partial differential equation for the rank one convex envelope
Adam M. Oberman, Yuanlong Ruan
In this article we introduce a Partial Differential Equation (PDE) for the rank one convex envelope. Rank one convex envelopes arise in non-convex vector valued variational problem…