Within the framework of Hilbert spaces, we solve nonlocal problems in bounded domains
with prescribed conditions on the complement of the domain. Our main focus is on the …

We prove trace and extension results for fractional Sobolev spaces of order s∈(0, 1). These
spaces are used in the study of nonlocal Dirichlet and Neumann problems on bounded …

This thesis explores the $ L^ 2$-Theory for nonlocal operators of L\'evy type on bounded
domains, as well as their local counterparts. The research was completed at Bielefeld …

We study nonlocal elliptic and parabolic equations on open sets in weighted Sobolev
spaces, where. The operators we consider are infinitesimal generators of symmetric stable …

In this paper we look at a probabilistic approach to a non‐local quadratic form that has lately
attracted some interest. This form is related to a recently introduced non‐local normal …

We give Martin representation of nonnegative functions caloric with respect to the fractional
Laplacian in Lipschitz open sets. The caloric functions are defined in terms of the mean …

We prove trace and extension results for Sobolev-type function spaces that are well suited
for nonlocal Dirichlet and Neumann problems including those for the fractional $ p …

Optimal Hardy inequality for the fractional Laplacian on Lp - ScienceDirect Skip to main
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For a given Lipschitz domain Ω, it is a classical result that the trace space of W 1, p (Ω) is W
1− 1/p, p (∂ Ω), namely any W 1, p (Ω) function has a well-defined W 1− 1/p, p (∂ Ω) trace …

Let $ D $ be a bounded $ C^ 2$-domain. Consider the following Dirichlet initial-boundary
problem of nonlocal operators with a drift: $$\partial_t u={\mathscr L}^{(\alpha)} _\kappa u+ …