# Global Schauder theory for minimizers of the $H^s(\Omega)$ energy

@inproceedings{Fall2021GlobalST, title={Global Schauder theory for minimizers of the \$H^s(\Omega)\$ energy}, author={Mouhamed Moustapha Fall and Xavier Ros-Oton}, year={2021} }

We study the regularity of minimizers of the functional E(u) := [u]2Hs(Ω)+ ∫ Ω fu. This corresponds to understanding solutions for the regional fractional Laplacian in Ω ⊂ R . More precisely, we are interested on the global (up to the boundary) regularity of solutions, both in the case of free minimizers in H(Ω) (i.e., Neumann problem), or in the case of Dirichlet condition u ∈ H 0(Ω) when s > 1 2 . Our main result establishes the sharp regularity of solutions in both cases: u ∈ C(Ω) in the…

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