150 research outputs found
Existence results for nonlinear elliptic problems on fractal domains
Some existence results for a parametric Dirichlet problem defined on the
Sierpi\'nski fractal are proved. More precisely, a critical point result for
differentiable functionals is exploited in order to prove the existence of a
well determined open interval of positive eigenvalues for which the problem
admits at least one non-trivial weak solution
Identification and Estimation of Preference Distributions When Voters Are Ideological
This paper studies the nonparametric identification and estimation of voters' preferences when voters are ideological. We build on the methods introduced by Degan and Merlo (2009) representing elections as Voronoi tessellations of the ideological space. We exploit the properties of this geometric structure to establish that voter preference distributions and other parameters of interest can be identified from aggregate electoral data. We also show that these objects can be consistently estimated using the methodology proposed by Ai and Chen (2003) and we illustrate our analysis by performing an actual estimation using data from the 1999 European Parliament elections.Voting, Voronoi tessellation,identification, nonparametric
Nonlinear problems on the Sierpi\'nski gasket
This paper concerns with a class of elliptic equations on fractal domains
depending on a real parameter. Our approach is based on variational methods.
More precisely, the existence of at least two non-trivial weak (strong)
solutions for the treated problem is obtained exploiting a local minimum
theorem for differentiable functionals defined on reflexive Banach spaces. A
special case of the main result improves a classical application of the
Mountain Pass Theorem in the fractal setting, given by Falconer and Hu (1999)
Twisted Alexander polynomials and incompressible surfaces given by ideal points
We study incompressible surfaces constructed by Culler-Shalen theory in the
context of twisted Alexander polynomials. For a st cohomology class of a
-manifold the coefficients of twisted Alexander polynomials induce regular
functions on the -character variety. We prove that if an
ideal point gives a Thurston norm minimizing non-separating surface dual to the
cohomology class, then the regular function of the highest degree has a finite
value at the ideal point.Comment: 10 pages, to appear in "The special issue for the 20th anniversary",
the Journal of Mathematical Sciences, the University of Toky
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