Function spaces in Lipschitz domains and on Lipschitz manifolds

By Hans Triebel. 2002

215 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1baf810205aa601a4947225ebe7d64ec4fea8f56

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In Mathematical Physics

Citations in the corpus

Fractional Sobolev extension and imbedding (2014, background): “Due to the applications, it attracts a lot of attention to extend fractional Sobolev (and also Besov and Triebel-Lizorkin) functions on a domain to the entire R n continuously; see [4, 16, 17, 23–25, 27, 29, 30].”
A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains (2009, unknown): “ the space H˚s(Ω) satisﬁes H˚s(Ω) = Hs z(Ω) if s>−1/2,s/∈ 1 2 +N0 . (2.12) For a Lipschitz domain Ω ⊆ Rn with compact boundary it is also known that Hs(Ω) ∗ = H−s(Ω), −1/2 <s<1/2. (2.13) See [124] for this and other related properties. Throughout this paper we agree to use the adjoint (rath”
Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities (2008, background): “ Hs(Rn), in relation to (3.3). One also has Hs 0(Ω) ∗ = H−s(Ω), s ∈ R (3.8) (cf., e.g., [33]). For a bounded Lipschitz domain Ω ⊂ Rn it is known that Hs(Ω) ∗ = H−s(Ω), −1/2 < s < 1/2. (3.9) See [51] for this and other related properties. To discuss Sobolev spaces on the boundary of a Lipschitz”
A Hölder infinity Laplacian (2012, unknown): “11 in [20] (for bounded and Lipschitz Ω) there is an extension of u to R , still named u, such that ‖u‖Bs p,p(R ) ≤ C ′‖u‖Bs p,p(Ω) ≤ C‖u‖W s,p(Ω).”
Generalized Robin Boundary Conditions, Robin-to-Dirichlet Maps, and Krein-Type Resolvent Formulas for Schr\ (2008, background): “family of open sets Ωj, 1 ≤ j≤ N, such that Ω = [N j=1 Ωj, Ωj star-like Lipschitz domain, 1 ≤ j≤ N. (A.6) For a Lipschitz domain Ω ⊂ Rn it is known that Hs(Ω) ∗ = H−s(Ω), −1/2 <s<1/2. (A.7) See [99] for this and other related properties. We also refer to our convention of using the adjoint (ra”
Non-self-adjoint operators, infinite determinants, and some applications (2005, background): “See [59] for this and other related properties.”
The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains (2008, unknown): “We refer the reader to [12], [27], [37], [39], [47], [58], for a more detailed exposition of these and other related matters.”
Function Spaces in Lipschitz Domains and Optimal Rates of Convergence for Sampling (2006, background): “5] and to [21] where these spaces are studied in bounded smooth domains and in bounded Lipschitz domains, respectively.”