Special Session 70: Progress and Challenges in Nonlocal and Nonhomogeneous PDEs

Fractional Orlicz-Sobolev Spaces: Embeddings \& Continuity properties
Angela Alberico
Italian National Research Council - Institute for Applied Calculus (Napoli)
Italy
Co-Author(s):    Lubos Pick and Lenka Slavikova
Abstract:
The optimal target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces. Both the subcritical and the supercritical regimes are considered. In the former case, the smallest possible Orlicz target space is detected. In the latter, the relevant Orlicz-Sobolev spaces are shown to be embedded into the space of bounded continuous functions in $\mathbb R^n$. Moreover, their optimal modulus of continuity is exhibited. These results are the subject of a series of joint papers with Andrea Cianchi, Lubo\v s Pick and Lenka Slav\'ikov\'a.