Math. Model. Nat. Phenom.
Volume 14, Number 5, 2019
Nonlocal and delay equations
|Number of page(s)||11|
|Published online||04 April 2019|
On spectral and boundary properties of the volume potential for the Helmholtz equation★
Institute of Mathematics and Mathematical Modelling,
125 Pushkin Str.,
2 Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Gent, Belgium.
3 School of Mathematical Sciences, Queen Mary University of London, London, UK.
4 Department of Mathematics, Nazarbayev University, 53 Kabanbay batyr Ave., Astana 010000, Kazakhstan.
* Corresponding author: firstname.lastname@example.org
Accepted: 27 December 2018
In this paper, we study boundary properties and some questions of spectral geometry for certain volume potential type operators (Bessel potential operators) in an open bounded Euclidean domains. In particular, the results can be valid for differential operators, which are related to a nonlocal boundary value problem for the Helmholtz equation, so we obtain isoperimetric inequalities for its eigenvalues as well, namely, analogues of the Rayleigh-Faber-Krahn inequality.
Mathematics Subject Classification: 35P99 / 47G40 / 35S15
Key words: Helmholtz equation / boundary value problem / Bessel potential / Schatten p-norm / Rayleigh-Faber-Krahn inequality
The first author was supported in parts by the MESRK grant BR05236656. The second author was supported in parts by the FWO Odysseus Project, by the EPSRC grant EP/R003025/1 and by the Leverhulme Grant RPG-2017-151. The third author was partially supported by the NU SPG and the MESRK grant AP05130981.
© EDP Sciences, 2019
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