The fractional Laplacian in R d, which we write as (− Δ) α/2 with α∈(0, 2), has multiple
equivalent characterizations. Moreover, in bounded domains, boundary conditions must be …

Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

The fractional Laplacian in R^ d has multiple equivalent characterizations. Moreover, in
bounded domains, boundary conditions must be incorporated in these characterizations in …

In this work we consider a generalized bilevel optimization framework for solving inverse
problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction …

SUMMARY A growing body of applied mathematics literature in recent years has focused on
the application of fractional calculus to problems of anomalous transport. In these analyses …

Fractional differential operators provide an attractive mathematical tool to model effects with
limited regularity properties. Particular examples are image processing and phase field …

In this work, we propose novel discretizations of the spectral fractional Laplacian on
bounded domains based on the integral formulation of the operator via the heat-semigroup …

Abstract Very recently Warma (2019 SIAM J. Control Optim. to appear) has shown that for
nonlocal PDEs associated with the fractional Laplacian, the classical notion of controllability …

We introduce and analyze a symmetric low-regularity scheme for the nonlinear Schrödinger
(NLS) equation beyond classical Fourier-based techniques. We show fractional …

We propose a new variational model in weighted Sobolev spaces with nonstandard weights
and applications to image processing. We show that these weights are, in general, not of …