Spectral results for mixed problems and fractional elliptic operators,

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Standard

Spectral results for mixed problems and fractional elliptic operators, / Grubb, Gerd.

I: Journal of Mathematical Analysis and Applications, Bind 421 , Nr. 2, 2015, s. 1616-1634.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Grubb, G 2015, 'Spectral results for mixed problems and fractional elliptic operators,', Journal of Mathematical Analysis and Applications, bind 421 , nr. 2, s. 1616-1634. https://doi.org/10.1016/j.jmaa.2014.07.081

APA

Grubb, G. (2015). Spectral results for mixed problems and fractional elliptic operators, Journal of Mathematical Analysis and Applications, 421 (2), 1616-1634. https://doi.org/10.1016/j.jmaa.2014.07.081

Vancouver

Grubb G. Spectral results for mixed problems and fractional elliptic operators, Journal of Mathematical Analysis and Applications. 2015; 421 (2):1616-1634. https://doi.org/10.1016/j.jmaa.2014.07.081

Author

Grubb, Gerd. / Spectral results for mixed problems and fractional elliptic operators,. I: Journal of Mathematical Analysis and Applications. 2015 ; Bind 421 , Nr. 2. s. 1616-1634.

Bibtex

@article{97f1846ab17748c6a3325f5080c0783d,
title = "Spectral results for mixed problems and fractional elliptic operators,",
abstract = "In the first part of the paper we show Weyl type spectral asymptotic formulas for pseudodifferential operators P a of order 2a, with type and factorization index a ∈ R+, restricted to compact sets with boundary; this includes fractional powers of the Laplace operator. The domain and the regularity of eigenfunctions is described. In the second part, we apply this in a study of realizations Aχ,Σ+ in L2(Ω) of mixed problems for a second-order strongly elliptic symmetric differential operator A on a bounded smooth set Ω ⊂ Rn; here the boundary ∂Ω=Σ is partioned smoothly into Σ=Σ_∪Σ+, the Dirichlet condition γ0u=0 is imposed on Σ_, and a Neumann or Robin condition χu=0 is imposed on Σ+. It is shown that the Dirichlet-to-Neumann operator Pγ,χ is principally of type 1/2 with factorization index 1/2, relative to Σ+. The above theory allows a detailed description of D (Aχ,Σ_+) with singular elements outside of Η3/2 (Ω), and leads to a spectral asymptotic formula for the Krein resolvent difference A −1χ,Σ_+ − A−1ϒ. ",
keywords = "Faculty of Science, matematik",
author = "Gerd Grubb",
year = "2015",
doi = "10.1016/j.jmaa.2014.07.081",
language = "English",
volume = " 421 ",
pages = "1616--1634",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press",
number = "2",

}

RIS

TY - JOUR

T1 - Spectral results for mixed problems and fractional elliptic operators,

AU - Grubb, Gerd

PY - 2015

Y1 - 2015

N2 - In the first part of the paper we show Weyl type spectral asymptotic formulas for pseudodifferential operators P a of order 2a, with type and factorization index a ∈ R+, restricted to compact sets with boundary; this includes fractional powers of the Laplace operator. The domain and the regularity of eigenfunctions is described. In the second part, we apply this in a study of realizations Aχ,Σ+ in L2(Ω) of mixed problems for a second-order strongly elliptic symmetric differential operator A on a bounded smooth set Ω ⊂ Rn; here the boundary ∂Ω=Σ is partioned smoothly into Σ=Σ_∪Σ+, the Dirichlet condition γ0u=0 is imposed on Σ_, and a Neumann or Robin condition χu=0 is imposed on Σ+. It is shown that the Dirichlet-to-Neumann operator Pγ,χ is principally of type 1/2 with factorization index 1/2, relative to Σ+. The above theory allows a detailed description of D (Aχ,Σ_+) with singular elements outside of Η3/2 (Ω), and leads to a spectral asymptotic formula for the Krein resolvent difference A −1χ,Σ_+ − A−1ϒ.

AB - In the first part of the paper we show Weyl type spectral asymptotic formulas for pseudodifferential operators P a of order 2a, with type and factorization index a ∈ R+, restricted to compact sets with boundary; this includes fractional powers of the Laplace operator. The domain and the regularity of eigenfunctions is described. In the second part, we apply this in a study of realizations Aχ,Σ+ in L2(Ω) of mixed problems for a second-order strongly elliptic symmetric differential operator A on a bounded smooth set Ω ⊂ Rn; here the boundary ∂Ω=Σ is partioned smoothly into Σ=Σ_∪Σ+, the Dirichlet condition γ0u=0 is imposed on Σ_, and a Neumann or Robin condition χu=0 is imposed on Σ+. It is shown that the Dirichlet-to-Neumann operator Pγ,χ is principally of type 1/2 with factorization index 1/2, relative to Σ+. The above theory allows a detailed description of D (Aχ,Σ_+) with singular elements outside of Η3/2 (Ω), and leads to a spectral asymptotic formula for the Krein resolvent difference A −1χ,Σ_+ − A−1ϒ.

KW - Faculty of Science

KW - matematik

U2 - 10.1016/j.jmaa.2014.07.081

DO - 10.1016/j.jmaa.2014.07.081

M3 - Journal article

VL - 421

SP - 1616

EP - 1634

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -

ID: 126422901