Interior regularity of solutions of non-local equations in Sobolev and Nikol’skii spaces

By Matteo Cozzi. 2016

59 citations recorded by the source corpus.

We prove interior $$H^{2 s - \varepsilon }$$H2s-ε regularity for weak solutions of linear elliptic integro-differential equations close to the fractional s-Laplacian. The result is obtained via intermediate estimates in Nikol’skii spaces, which are in turn carried out by means of an appropriate modification of the classical translation method by Nirenberg.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/22a2a983222b6003f6d8e86a84e9603195f24904

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Local Elliptic Regularity for the Dirichlet Fractional Laplacian (2017, background): “∙ In [6], it is proved that if we take f ∈ L2(Ω), then the corresponding weak solution of (1.”
Higher Hölder regularity for the fractional p-Laplacian in the superquadratic case (2017, result): “There has also been some recent progress in terms of higher differentiability of the solutions: in [27] and [14] the case p = 2 is treated (also for a more general kernel K(x, y), not necessarily given by |x− y| ), while for a general p ≥ 2 results in this sense have been obtained by the third autho”
Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case (2015, background): “Some results on this subject are contained in the recent papers [9, 17] and [25] (see also [19]).”