Sobolev W1p -spaces on d-thick closed subsets of Rn Full article
| Journal |
Sbornik Mathematics
ISSN: 1064-5616 , E-ISSN: 1468-4802 |
||||
|---|---|---|---|---|---|
| Output data | Year: 2020, Volume: 211, Number: 6, Pages: 786--837 Pages count : 52 DOI: 10.1070/SM9199 | ||||
| Tags | Sobolev spaces, Whitney problem, traces, extension operators. | ||||
| Authors |
|
||||
| Affiliations |
|
Abstract:
Let S ⊂ Rn be a nonempty closed set such that for some
d ∈ [0, n] and ε > 0 the d-Hausdorff content H d∞(S ∩ Q(x, r)) ⩾ εrd for
all cubes Q(x, r) with centre x ∈ S and edge length 2r ∈ (0, 2]. For each
p > max{1, n − d} we give an intrinsic characterization of the trace space
W1p (Rn)|S of the Sobolev space W1p (Rn) to the set S. Furthermore, we prove the existence of a bounded linear operator Ext: W1p (Rn)|S →W1p (Rn) such that Ext is the right inverse to the standard trace operator. Our results
extend those available in the case p ∈ (1, n] for Ahlfors-regular sets S
Cite:
Vodopyanov S.K.
, Tyulenev A.I.
Sobolev W1p -spaces on d-thick closed subsets of Rn
Sbornik Mathematics. 2020. V.211. N6. P.786--837. DOI: 10.1070/SM9199 WOS Scopus OpenAlex
Sobolev W1p -spaces on d-thick closed subsets of Rn
Sbornik Mathematics. 2020. V.211. N6. P.786--837. DOI: 10.1070/SM9199 WOS Scopus OpenAlex
Original:
Водопьянов С.К.
, Тюленев А.И.
Пространства Соболева W1 p на d-толстых замкнутых подмножествах Rn
Математический сборник. 2020. Т.211. №6. С.40-94. DOI: 10.4213/sm9199 OpenAlex
Пространства Соболева W1 p на d-толстых замкнутых подмножествах Rn
Математический сборник. 2020. Т.211. №6. С.40-94. DOI: 10.4213/sm9199 OpenAlex
Dates:
| Submitted: | Nov 27, 2018 |
| Accepted: | Feb 14, 2020 |
Identifiers:
| Web of science: | WOS:000564139800001 |
| Scopus: | 2-s2.0-85094592409 |
| OpenAlex: | W3010674122 |