This book is the first volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

We prove Besov regularity estimates for the solution of the Dirichlet problem involving the
integral fractional Laplacian of order s in bounded Lipschitz domains Ω:‖ u‖ B˙ 2,∞ s+ r …

The integral fractional Laplacian of order s∈(0,1) is a nonlocal operator. It is known that
solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary …

For the discretization of the integral fractional Laplacian $(-\Delta)^ s $, $0< s< 1$, based on
piecewise linear functions, we present and analyze a reliable weighted residual a posteriori …

This survey hinges on the interplay between regularity and approximation for linear and
quasilinear fractional elliptic problems on Lipschitz domains. For the linear Dirichlet integral …

We propose a monotone discretization for the integral fractional Laplace equation on
bounded Lipschitz domains with the homogeneous Dirichlet boundary condition. The …

This paper addresses the approximation of fractional harmonic maps. Besides a unit-length
constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness …

For first-order discretizations of the integral fractional Laplacian, we provide sharp local error
estimates on proper subdomains in both the local H^1-norm and the localized energy norm …

This work is an extension of the paper by Cea and Malanowski to the nonlocal and
nonlinear framework. The addressed topic is the study of an optimal control problem driven …