scholarly journals Towards a reversed Faber–Krahn inequality for the truncated Laplacian

2019 ◽  
Vol 36 (3) ◽  
pp. 723-740 ◽  
Author(s):  
Isabeau Birindelli ◽  
Giulio Galise ◽  
Hitoshi Ishii
Keyword(s):  
Krahn Inequality

On spectral and boundary properties of the volume potential for the Helmholtz equation

2019 ◽  
Vol 14 (5) ◽  
pp. 502
Author(s):  
Tynysbek Sharipovich Kalmenov ◽  
Michael Ruzhansky ◽  
Durvudkhan Suragan
Keyword(s):  
Helmholtz Equation ◽  
Differential Operators ◽  
Nonlocal Boundary ◽  
Spectral Geometry ◽  
Bessel Potential ◽  
Nonlocal Boundary Value Problem ◽  
Volume Potential ◽  
Potential Operators ◽  
Boundary Properties ◽  
Krahn Inequality

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.

scholarly journals Surgery of the Faber–Krahn inequality and applications to heat kernel bounds

2016 ◽  
Vol 131 ◽  
pp. 243-272 ◽  
Author(s):  
Alexander Grigor’yan ◽  
Laurent Saloff-Coste
Keyword(s):  
Heat Kernel ◽  
Kernel Bounds ◽  
Krahn Inequality

Faber-Krahn inequality on regular trees

1998 ◽  
Vol 91 (3) ◽  
pp. 463-514 ◽  
Author(s):  
Alexander R. Pruss
Keyword(s):  
Krahn Inequality

scholarly journals A quantitative stability estimate for the fractional Faber-Krahn inequality

2020 ◽  
Vol 279 (3) ◽  
pp. 108560 ◽  
Author(s):  
Lorenzo Brasco ◽  
Eleonora Cinti ◽  
Stefano Vita
Keyword(s):  
Stability Estimate ◽  
Quantitative Stability ◽  
Krahn Inequality

A Faber–Krahn Inequality for the Cheeger Constant of $$N$$ N -gons

2014 ◽  
Vol 26 (1) ◽  
pp. 88-117 ◽  
Author(s):  
Dorin Bucur ◽  
Ilaria Fragalà
Keyword(s):  
Cheeger Constant ◽  
Krahn Inequality
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