12,969 research outputs found
The Neumann problem in thin domains with very highly oscillatory boundaries
In this paper we analyze the behavior of solutions of the Neumann problem
posed in a thin domain of the type with and , defined by smooth
functions and , where the function is supposed to be
-periodic in the second variable . The condition implies
that the upper boundary of this thin domain presents a very high oscillatory
behavior. Indeed, we have that the order of its oscillations is larger than the
order of the amplitude and height of given by the small parameter
. We also consider more general and complicated geometries for thin
domains which are not given as the graph of certain smooth functions, but
rather more comb-like domains.Comment: 20 pages, 4 figure
Products of finite groups and nonmeasurable subgroups
It is proven that if is a finite group, then has dense nonmeasurable subgroups. Also, other examples of compact groups with
dense nonmeasurable subgroups are presented.Comment: 5 page
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The timing of capacity expansion investments in oligopoly under demand uncertainty
Since a flexibility value emerges in waiting to expand capacity, the impact of demand uncertainty in an oligopolistic industry leads to capacity expansion timing. The creation of growth opportunities is then the outcome of expanding capacity at optimal times. However, in our model different capacity size competitors interact not affecting each others, because assessing the impact of demand uncertainty on capacity expansion projects takes them to set up independently their optimal capacity expansion timing schedules. In equilibrium no firm expands capacity more often than any other. Under demand uncertainty simultaneity in capacity expansions is the only possible Markov Perfect Equilibrium
Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains
We consider the biharmonic operator subject to homogeneous boundary
conditions of Neumann type on a planar dumbbell domain which consists of two
disjoint domains connected by a thin channel. We analyse the spectral behaviour
of the operator, characterizing the limit of the eigenvalues and of the
eigenprojections as the thickness of the channel goes to zero. In applications
to linear elasticity, the fourth order operator under consideration is related
to the deformation of a free elastic plate, a part of which shrinks to a
segment. In contrast to what happens with the classical second order case, it
turns out that the limiting equation is here distorted by a strange factor
depending on a parameter which plays the role of the Poisson coefficient of the
represented plate.Comment: To appear in "Integral Equations and Operator Theory
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