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    Extending Sobolev functions with partially vanishing traces from locally (ε, δ)-domains and applications to mixed boundary problems

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    Genre
    Journal Article
    Date
    2014-04-01
    Author
    Brewster, K
    Mitrea, D
    Mitrea, I
    Mitrea, M
    Subject
    Higher-order Sobolev space
    Linear extension operator
    Locally (epsilon, delta)-domain
    Higher-order boundary trace operator
    Real and complex interpolation
    Besov and Triebel-Lizorkin spaces
    Bessel potential space and capacity
    Ahlfors regular set
    Synthesis
    Mixed boundary value problem
    Higher-order elliptic system
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    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5888
    
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    DOI
    10.1016/j.jfa.2014.02.001
    Abstract
    We prove that given any k∈N, for each open set Ω⊆Rn and any closed subset D of Ω- such that Ω is locally an (ε, δ)-domain near ∂Ω. D, there exists a linear and bounded extension operator Ek,D mapping, for each p∈. [1, ∞], the space WDk,p(Ω) into WDk,p(Rn). Here, with O denoting either Ω or Rn, the space WDk,p(O) is defined as the completion in the classical Sobolev space Wk,p(O) of (restrictions to O of) functions from Cc∞(Rn) whose supports are disjoint from D. In turn, this result is used to develop a functional analytic theory for the class WDk,p(Ω) (including intrinsic characterizations, boundary traces and extensions results, interpolation theorems, among other things) which is then employed in the treatment of mixed boundary value problems formulated in locally (ε, δ)-domains. Finally, we also prove extension results on the scales of Besov and Bessel potential spaces on (ε, δ)-domains with partially vanishing traces on Ahlfors regular sets and explore some of the implications of such extension results. © 2014 Elsevier Inc.
    Citation to related work
    Elsevier BV
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    Journal of Functional Analysis
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5870
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