Abstract
AbstractWe construct whole-space extensions of functions in a fractional Sobolev space of order $$s\in (0,1)$$
s
∈
(
0
,
1
)
and integrability $$p\in (0,\infty )$$
p
∈
(
0
,
∞
)
on an open set O which vanish in a suitable sense on a portion D of the boundary $${{\,\mathrm{\partial \!}\,}}O$$
∂
O
of O. The set O is supposed to satisfy the so-called interior thickness condition in$${{\,\mathrm{\partial \!}\,}}O {\setminus } D$$
∂
O
\
D
, which is much weaker than the global interior thickness condition. The proof works by means of a reduction to the case $$D=\emptyset $$
D
=
∅
using a geometric construction.
Funder
Studienstiftung des Deutschen Volkes
Publisher
Springer Science and Business Media LLC
Reference11 articles.
1. Bechtel, S., Egert, M., Haller-Dintelmann, R.: The Kato square root problem on locally uniform domains. Adv. Math. 375, 107410 (2020)
2. Dahlke, S., Hansen, M., Schneider, C., Sickel, W.: Properties of Kondratiev spaces. Preprint (2019)
3. Dyda, B., Vähäkangas, A.: A framework for fractional Hardy inequalities. Ann. Acad. Sci. Fenn. Math. 39(2), 675–689 (2014)
4. Egert, M., Haller-Dintelmann, R., Rehberg, J.: Hardy’s inequality for functions vanishing on a part of the boundary. Potential Anal. 43, 49–78 (2015)
5. Egert, M., Tolksdorf, P.: Characterizations of Sobolev functions that vanish on a part of the boundary. Discrete Contin. Dyn. Syst. Ser. S 10(4), 729–743 (2017)
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Interlude: Extension Operators for Fractional Sobolev Spaces;Operator Theory: Advances and Applications;2024
2. Introduction;Operator Theory: Advances and Applications;2024
3. On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains;Proceedings of the Steklov Institute of Mathematics;2023-12
4. О регулярности характеристических функций слабо внешне толстых областей;Труды Математического института имени В. А. Стеклова;2023-12