Juan Pablo Borthagaray

Universidad de La Republica, Uruguay

Title: Finite element approximation of a fractional p-Laplacian

Abstract: This talk explores the numerical treatment of the fractional $p$-Laplace operator ($p\in (1,\infty)$), which arises in the complex interpolation of Sobolev spaces. When $p=2$, it coincides with the usual fractional Laplacian, but for $p\neq 2$ it differs from the $(p,s)$-Laplacian obtained via real interpolation between Sobolev spaces. We present a decomposition-coordination method using an augmented Lagrangian formulation to compute solutions and their fractional gradients, along with an analysis of its convergence and practical implementation.