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Eigenvalues control for a Finsler--Laplace operator
Eigenvalues control Finsler--Laplace operator Differential Geometry
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2012/6/27
Using the definition of a Finsler--Laplacian given by the first author, we show that two bi-Lipschitz Finsler metrics have a controlled spectrum. We deduce from that several generalizations of Riemann...
Eigenvalues of the fractional Laplace operator in the interval
Eigenvalues fractional Laplace operator interval
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2011/1/18
Two-term Weyl-type asymptotic law for the eigenvalues of one-dimensional fractional Laplace operator (−) /2 ( ∈ (0, 2)) in the interval (−1, 1) is given: the n-th eigenvalue is equal to ...
The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator
Bessel Laplace operator Bessel Helmholtz operator
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2010/9/25
It is found that the existence of the solution u(x) of such equation depending on the condition of f and k−1 B (B+m2)ku(x). Moreover such solution u(x) related to the nonhomogeneous Bessel bih...
Behavior of the singular solutions of the problem governed by the adjunct of the Laplace operator affected by a weight function near the tops of plane polygon
Singularity Polygon function
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2010/9/21
In this work, we study the behavior of the singular solutions of the problem governed by the adjunct of the laplacian operator affected by a weight function in a polygon. First, the study will be done...
Sharp Constants for Some Inequalities Connected to the $p$-Laplace Operator
$p$-Poisson $p$-Laplace Inequalities Sharp constants Structure conditions
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2008/6/26
In this paper we investigate a set of structure conditions used in the existence theory of differential equations. More specific, we find best constants for the corresponding inequalities in the speci...
ASYMPTOTIC OF EIGENVALUES OF THE $p$-LAPLACE OPERATOR AND LATTICE POINTS
$p$-Laplacian eigenvalues lattice points
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2007/12/12
In this work we study the spectral counting function for the $p$-Laplace operator in one dimension. We show the existence of a two-term Weyl-type asymptote. The method of proof is rather elementary, b...