In:
Advanced Nonlinear Studies, Walter de Gruyter GmbH, Vol. 17, No. 4 ( 2017-11-01), p. 837-839
Abstract:
In [1], for 1 〈 p 〈 ∞ {1 〈 p 〈 \infty} , we proved the W loc 2 s , p {W^{2s,p}_{\mathrm{loc}}} local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian ( - Δ ) s {(-\Delta)^{s}} on an arbitrary bounded open set of ℝ N {\mathbb{R}^{N}} . Here we make a more precise and rigorous statement. In fact, for 1 〈 p 〈 2 {1 〈 p 〈 2} and s ≠ 1 2 {s\neq\frac{1}{2}} , local regularity does not hold in the Sobolev space W loc 2 s , p {W^{2s,p}_{\mathrm{loc}}} , but rather in the larger Besov space ( B p , 2 2 s ) loc {(B^{2s}_{p,2})_{\mathrm{loc}}} .
Type of Medium:
Online Resource
ISSN:
1536-1365
,
2169-0375
DOI:
10.1515/ans-2017-6020
Language:
English
Publisher:
Walter de Gruyter GmbH
Publication Date:
2017
detail.hit.zdb_id:
2482156-1
SSG:
17,1
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