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math.NA2016
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…
math.AP2016
Explicit Equilibrium Solutions For the Aggregation Equation with Power-Law Potentials
José A. Carrillo, Yanghong Huang
Despite their wide presence in various models in the study of collective behaviors, explicit swarming patterns are difficult to obtain. In this paper, special stationary solutions…