Inequalities for Dirichlet and Neumann eingenvalues of the laplacian for domains on spheres
M. Ashbaugh, Howard A. Levine (1997)
Journées équations aux dérivées partielles
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M. Ashbaugh, Howard A. Levine (1997)
Journées équations aux dérivées partielles
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Parini, Enea (2010)
International Journal of Differential Equations
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Isaac Chavel, Edgar A. Feldman (1974)
Compositio Mathematica
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Sylvestre Gallot (1986-1987)
Séminaire de théorie spectrale et géométrie
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Zayed, E.M.E., Younis, A.I. (1995)
International Journal of Mathematics and Mathematical Sciences
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Zayed, E.M.E. (1993)
International Journal of Mathematics and Mathematical Sciences
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Kwean, Hyukjin (2001)
International Journal of Mathematics and Mathematical Sciences
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David Krejčiřík (2009)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet...
Martínez, Sandra, Rossi, Julio D. (2002)
Abstract and Applied Analysis
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Kei Funano (2016)
Analysis and Geometry in Metric Spaces
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We apply Gromov’s ham sandwich method to get: (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in Euclidean space.