Variational solutions to nonlocal problems (Q776400)

A class of linear and unbounded nonlocal operators on \(L^2(\mathbb{R}^d)\) ise studied. Similarities and differences with regard to the theory of differential operators of second order is explained, focusing on stationary linear symmetric operators in various forms. Variational solutions are provided to the nonlocal Dirichlet problem of fractional order. Local regularity of nonlocal operators is studied using (weak) Harnack inequalities and Hölder regularity. Analogies and differences between local and nonlocal operators are explained. For the entire collection see [Zbl 1416.60012].