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Fractional eigenvalue problems that approximate Steklov eigenvalue problems

Part of: Elliptic equations and systems Eigenvalue problems Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  28 December 2017

Leandro M. Del Pezzo ,
Julio D. Rossi  and
Ariel M. Salort
Leandro M. Del Pezzo
Affiliation:
Departamento de Matemática and Instituto de Investigaciones Matemáticas ‘Luis A. Santaló’, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428), Av. Cantilo s/n. Buenos Aires, Argentina (ldpezzo@dm.uba.ar; jrossi@dm.uba.ar; asalort@dm.uba.ar)
Julio D. Rossi
Affiliation:
Departamento de Matemática and Instituto de Investigaciones Matemáticas ‘Luis A. Santaló’, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428), Av. Cantilo s/n. Buenos Aires, Argentina (ldpezzo@dm.uba.ar; jrossi@dm.uba.ar; asalort@dm.uba.ar)
Ariel M. Salort
Affiliation:
Departamento de Matemática and Instituto de Investigaciones Matemáticas ‘Luis A. Santaló’, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428), Av. Cantilo s/n. Buenos Aires, Argentina (ldpezzo@dm.uba.ar; jrossi@dm.uba.ar; asalort@dm.uba.ar)
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Abstract

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In this paper we analyse possible extensions of the classical Steklov eigenvalue problem to the fractional setting. In particular, we find a non-local eigenvalue problem of fractional type that approximates, when taking a suitable limit, the classical Steklov eigenvalue problem.

Keywords

Steklov eigenvaluesnonlocal problemsSobolev inequalities

MSC classification

Secondary: 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory 35J61: Semilinear elliptic equations 45C05: Eigenvalue problems
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 3 , June 2018 , pp. 499 - 516
Copyright
Copyright © Royal Society of Edinburgh 2018