10,610 research outputs found
Neumann to Steklov eigenvalues: asymptotic and monotonicity results
We consider the Steklov eigenvalues of the Laplace operator as limiting
Neumann eigenvalues in a problem of mass concentration at the boundary of a
ball. We discuss the asymptotic behavior of the Neumann eigenvalues and find
explicit formulas for their derivatives at the limiting problem. We deduce that
the Neumann eigenvalues have a monotone behavior in the limit and that Steklov
eigenvalues locally minimize the Neumann eigenvalues.Comment: This paper has been accepted for publication in Proceedings of the
Royal Society of Edinburgh Section A Mathematics and will appear in a revised
form subsequent to editorial input by the ICMS/Royal Soc. of Edinburgh.
Material on these pages is copyright Cambridge University Press.
http://www.rsescotlandfoundation.org.uk/proceedings-a-mathematics.html
journals.cambridge.org/action/displayJournal?jid=PR
Telegram from Ralph Lamberti, Deputy Borough President of Staten Island, to Geraldine Ferraro
Congratulatory telegram from Ralph J. Lamberti, Deputy Borough President of Staten Island, to Geraldine Ferraro. Includes standard response letter from Ferraro, and a data entry sheet.https://ir.lawnet.fordham.edu/vice_presidential_campaign_correspondence_1984_new_york/1266/thumbnail.jp
A maximum principle in spectral optimization problems for elliptic operators subject to mass density perturbations
We consider eigenvalue problems for general elliptic operators of arbitrary
order subject to homogeneous boundary conditions on open subsets of the
euclidean N-dimensional space. We prove stability results for the dependence of
the eigenvalues upon variation of the mass density and we prove a maximum
principle for extremum problems related to mass density perturbations which
preserve the total mass
Shape sensitivity analysis of the Hardy constant
We consider the Hardy constant associated with a domain in the
-dimensional Euclidean space and we study its variation upon perturbation of
the domain. We prove a Fr\'{e}chet differentiability result and establish a
Hadamard-type formula for the corresponding derivatives. We also prove a
stability result for the minimizers of the Hardy quotient. Finally, we prove
stability estimates in terms of the Lebesgue measure of the symmetric
difference of domains.Comment: 23 pages; showkeys command remove
An H-theorem for the Brownian motion on the hyperbolic plane
We prove an theorem for the Brownian motion on the hyperbolic plane with
a drift, as studied by Comtet and Monthus; the entropy used here is not the
Boltzmann entropy but the R\'enyi entropy, the parameter of which being related
in a simple way to the value of the drift.Comment: Better versio
Sobolev subspaces of nowhere bounded functions
We prove that in any Sobolev space which is subcritical with respect to the Sobolev Embedding Theorem there exists a closed infinite dimensional linear subspace whose non zero elements are nowhere bounded functions. We also prove the existence of a closed infinite dimensional linear subspace whose non zero elements are nowhere Lq functions for suitable values of q larger than the Sobolev exponent
Spectral stability for a class of fourth order Steklov problems under domain perturbations
We study the spectral stability of two fourth order Steklov problems upon domain perturba- tion. One of the two problems is the classical DBS\u2014Dirichlet Biharmonic Steklov\u2014problem, the other one is a variant. Under a comparatively weak condition on the convergence of the domains, we prove the stability of the resolvent operators for both problems, which implies the stability of eigenvalues and eigenfunctions. The stability estimates for the eigenfunctions are expressed in terms of the strong H2-norms. The analysis is carried out without assuming that the domains are star-shaped. Our condition turns out to be sharp at least for the variant of the DBS problem. In the case of the DBS problem, we prove stability of a suitable Dirichlet- to-Neumann type map under very weak conditions on the convergence of the domains and we formulate an open problem. As bypass product of our analysis, we provide some stability and instability results for Navier and Navier-type boundary value problems for the biharmonic operator
Monotonicity, continuity and differentiability results for the Hardy constant
We consider the Hardy inequality involving the distance to the boundary
for a domain in the -dimensional Euclidean space. We study the dependence on
of the corresponding best constant and we prove monotonicity, continuity
and differentiability results. The focus is on non-convex domains in which case
such constant is in general not explicitly known.Comment: 12 pages; to appear in the Israel Journal of Mathematic
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