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Mat. Sb., 2014, Volume 205, Number 8, Pages 67–94 (Mi msb8311)  

This article is cited in 3 scientific papers (total in 3 papers)

Boundary values of functions in a Sobolev space with Muckenhoupt weight on some non-Lipschitz domains

A. I. Tyulenev

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: This paper gives an explicit description of the traces of functions in a weighted Sobolev space (with local Muckenhoupt weight) on the domain lying between two graphs of Lipschitz functions and on the complement of the closure of this domain.
Bibliography: 11 titles.

Keywords: Muckenhoupt weight, weighted Sobolev space, Besov spaces of variable smoothness, non-Lipschitz domains.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00744


DOI: https://doi.org/10.4213/sm8311

Full text: PDF file (622 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:8, 1133–1159

Bibliographic databases:

Document Type: Article
UDC: 517.538
MSC: 46E35
Received: 27.11.2013 and 17.04.2014

Citation: A. I. Tyulenev, “Boundary values of functions in a Sobolev space with Muckenhoupt weight on some non-Lipschitz domains”, Mat. Sb., 205:8 (2014), 67–94; Sb. Math., 205:8 (2014), 1133–1159

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v205/i8/p67

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. N. Dhara, A. Kałamajska, “On proper formulation of boundary condition for degenerated PDEs when trace embedding theorems are missing and application to nonhomogeneous BVPs”, Complex Var. Elliptic Equ., 61:11 (2016), 1541–1553  crossref  mathscinet  zmath  isi  scopus
    2. P. Koskela, T. Soto, Zh. Wang, “Traces of weighted function spaces: dyadic norms and Whitney extensions”, Sci. China Math., 60:11 (2017), 1981–2010  crossref  mathscinet  zmath  isi  scopus
    3. S. Dipierro, E. Valdinoci, “Continuity and density results for a one-phase nonlocal free boundary problem”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 34:6 (2017), 1387–1428  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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