Spectral results for mixed problems and fractional elliptic operators,
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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.
Translated title of the contribution | Spektrale resultater for blandede problemer og elliptiske operatorer af ikke-hel orden |
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Original language | English |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 421 |
Issue number | 2 |
Pages (from-to) | 1616-1634 |
ISSN | 0022-247X |
DOIs | |
Publication status | Published - 2015 |
- Faculty of Science
Research areas
ID: 126422901