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arXiv · 1601.02819

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

Matteo Cozzi
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Abstract

We prove interior $H^{2s-\varepsilon}$ 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.

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Matteo Cozzi. 2016-01-12. Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces. https://doi.org/10.1007/s10231-016-0586-3

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