Estimates for the parametrix of the Kohn Laplacian on certain domains.
Matei Machedon (1988)
Inventiones mathematicae
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Matei Machedon (1988)
Inventiones mathematicae
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Christopher B. Croke (1982)
Inventiones mathematicae
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Davide Buoso, Pier Domenico Lamberti (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider a class of eigenvalue problems for polyharmonic operators, including Dirichlet and buckling-type eigenvalue problems. We prove an analyticity result for the dependence of the symmetric functions of the eigenvalues upon domain perturbations and compute Hadamard-type formulas for the Frechét differentials. We also consider isovolumetric domain perturbations and characterize the corresponding critical domains for the symmetric functions of the eigenvalues. Finally, we prove...
Damian Wiśniewski, Mariusz Bodzioch (2016)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
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.
Peter Li, Jia Qing Zhong (1981/82)
Inventiones mathematicae
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Peter Li, Andrejs E. Treibergs (1982)
Inventiones mathematicae
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Shmuel Friedland (2015)
Special Matrices
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In this paper we give necessary and sufficient conditions for the equality case in Wielandt’s eigenvalue inequality.
Lucio Damascelli (2000)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We present a simple proof of the fact that if is a bounded domain in , , which is convex and symmetric with respect to orthogonal directions, , then the nodal sets of the eigenfunctions of the laplacian corresponding to the eigenvalues must intersect the boundary. This result was proved by Payne in the case for the second eigenfunction, and by other authors in the case of convex domains in the plane, again for the second eigenfunction.
D.E. Barrett (1986)
Inventiones mathematicae
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Jan Bochenek (1980)
Annales Polonici Mathematici
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