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pro vyhledávání: '"Harrell, Evans"'
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 March 2024 531(1) Part 2
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We use the averaged variational principle introduced in a recent article on graph spectra [7] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of Kr{\"o}ge
Externí odkaz:
http://arxiv.org/abs/1507.02632
Autor:
Soufi, Ahmad El, Harrell, Evans
We prove that among all doubly connected domains of $\R^n$ bounded by two spheres of given radii, $Z(t)$, the trace of the heat kernel with Dirichlet boundary conditions, achieves its minimum when the spheres are concentric (i.e., for the spherical s
Externí odkaz:
http://arxiv.org/abs/1402.3900
We focus on the analysis of local minimizers of the Mahler volume, that is to say the local solutions to the problem $$\min\{ M(K):=|K||K^\circ|\;/\;K\subset\R^d\textrm{ open and convex}, K=-K\}, $$ where $K^\circ:=\{\xi\in\R^d ; \forall x\in K, x\cd
Externí odkaz:
http://arxiv.org/abs/1104.3663
Autor:
Harrell, Evans, Henrot, Antoine
We consider a family of functionals $J$ to be maximized over the planar convex sets $K$ for which the perimeter and Steiner point have been fixed. Assuming that $J$ is the integral of a quadratic expression in the support function $h$, we show that t
Externí odkaz:
http://arxiv.org/abs/0905.1464
Publikováno v:
Transactions of the American Mathematical Society 361, 5 (2009) 2337--2350
We establish inequalities for the eigenvalues of Schr\"odinger operators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, complex and quaternionic projective spaces, which are related to inequali
Externí odkaz:
http://arxiv.org/abs/0902.1923
Autor:
Harrell, Evans M., Hermi, Lotfi
In this article we prove the equivalence of certain inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian with a classical inequality of Kac. Connections are made via integral transforms including those of Laplace, Legendre, Weyl, an
Externí odkaz:
http://arxiv.org/abs/0712.4088
Publikováno v:
Lett. Math. Phys. 75 (2006), 225-233 ; addendum 75 (2006), 219
We consider a pair of isoperimetric problems arising in physics. The first concerns a Schr\"odinger operator in $L^2(\mathbb{R}^2)$ with an attractive interaction supported on a closed curve $\Gamma$, formally given by $-\Delta-\alpha \delta(x-\Gamma
Externí odkaz:
http://arxiv.org/abs/math-ph/0508060
Autor:
Harrell, Evans M.
An extension of the lower-bound lemma of Boggio is given for the weak forms of certain elliptic operators, which have partially Dirichlet and partially Neumann boundary conditions, and are in general nonlinear. Its consequences and those of an adapte
Externí odkaz:
http://arxiv.org/abs/math/0407465