Rayleigh–Faber–Krahn, Lyapunov and Hartmann–Wintner Inequalities for Fractional Elliptic Problems
Kassymov A. Ruzhansky M. Torebek B.T.
June 2023Birkhauser
Mediterranean Journal of Mathematics
2023#20Issue 3
In this paper, in the cylindrical domain, we consider a fractional elliptic operator with Dirichlet conditions. We prove, that the first eigenvalue of the fractional elliptic operator is minimised in a circular cylinder among all cylindrical domains of the same Lebesgue measure. This inequality is called the Rayleigh–Faber–Krahn inequality. Also, we give Lyapunov and Hartmann–Wintner inequalities for the fractional elliptic boundary value problem.
Caputo derivative , fractional order differential operator , Hartman–Wintner inequality , Lyapunov inequality , Rayleigh–Faber–Krahn inequality , Riemann–Liouville derivative
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Ghent University, Ghent, Belgium
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Queen Mary University of London, London, United Kingdom
Ghent University
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
Queen Mary University of London
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