We prove interior 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.
Interior regularity of solutions of non-local equations in Sobolev and Nikol’skii spaces / M. Cozzi. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 196:2(2017), pp. 555-578. [10.1007/s10231-016-0586-3]
Interior regularity of solutions of non-local equations in Sobolev and Nikol’skii spaces
M. Cozzi
2017
Abstract
We prove interior 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.
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