Linear and nonlinear fractional elliptic problems
Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto · Contemporary mathematics - American Mathematical Society · 2020
This paper surveys recent analytical and numerical research on linear problems for the integral fractional Laplacian, fractional obstacle problems, and fractional minimal graphs. The emphasis is on the interplay between regularity, including boundary behavior, and approximability by piecewise linear finite element methods. We discuss several error estimates on graded meshes, and computational challenges associated to implementing and solving efficiently the ensuing integral equations, along with numerical experiments.