Quaderni di Dipartimento
Collezione dei preprint del Dipartimento di Matematica.
La presenza del full-text è lacunosa per i prodotti antecedenti maggio 2006.
Trovati 868 prodotti
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QDD32 - 13/05/2008
Gazzola, Filippo ; Pierotti, Dario
Positive solutions to critical growth biharmonic elliptic problems under Steklov boundary conditions | Abstract | | We study the fourth order nonlinear critical problem Delta^2u = u^{2^*-1} in the unit ball of R^n (n ge 5), subject to the Steklov boundary conditions u = Delta u-d u_{ nu}=0 on partial B.
We provide the exact range of the parameter d for which this problem admits a positive (radial) solution. We also show that the solution is unique in this range and in the class of radially symmetric functions. Finally, we study the behavior of the solution when d tends to the extremals of this range. These results complement previous results in [3]. |
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QDD33 - 13/05/2008
Gazzola, F. ; Grunau, H.C. ; Mitidieri, E.
Hardy inequalities with optimal constants and remainder terms | Abstract | | We show that the classical Hardy inequalities with optimal constants in the Sobolev spaces $W_0^{1,p}$ and in higher-order Sobolev spaces on a bounded domain $ Omega subset mathbb{R}^n$ can be refined by adding remainder terms which involve $L^p$ norms. In the higher-order case further $L^p$ norms with lower-order singular weights arise. The case $1 |
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QDD30 - 10/04/2008
Biroli M. ; Marchi S.
Wiener criterion for relaxed problems related to p-homogeneous Riemannian Dirichlet forms | Abstract | | We state a Wiener criterion for the regularity of points with respect to a relaxed Dirichlet problem for a p-homogeneous Riemannian Dirichlet form. |
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QDD29 - 07/04/2008
Barchielli, A. ; Gregoratti, M. ; Licciardo, M.
Feedback control of the fluorescence light squeezing | Abstract | | We consider a two-level atom stimulated by a coherent monochromatic laser and we study how to
enhance the squeezing of the fluorescence light and of the atom itself in the presence of a Wiseman-Milburn feedback mechanism, based on the homodyne detection of a fraction of the emitted light. Besides analyzing the effect of the control parameters on the squeezing properties of the light and of the atom, we also discuss the relations among these. The problem is tackled inside the framework of quantum trajectory theory. |
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QDD28 - 26/03/2008
Bassetti, F. ; Ladelli, L. ; Regazzini, E.
Probabilistic study of the speed of approach to equilibrium for an inelastic Kac model | Abstract | | This paper deals with a one--dimensional model for granular materials, which boils down to an inelastic version of the Kac kinetic equation, with inelasticity parameter p>0. In particular, the paper provides bounds for certain distances -- such as specific weighted chi--distances and the Kolmogorov distance -- between the solution of that equation and the limit. It is assumed that the even part of the initial datum (which determines the asymptotic properties of the solution) belongs to the domain of normal attraction of a symmetric stable distribution with characteristic exponent alpha=2/(1+p). With such initial data, it turns out that the limit exists and is just the aforementioned stable distribution. A necessary condition for the relaxation to equilibrium is also proved. Some bounds are obtained without introducing any extra--condition. Sharper bounds, of an exponential type, are exhibited in the presence of additional assumptions concerning either the behaviour, near to the origin, of the initial characteristic function, or the behaviour, at infinity, of the initial probability distribution function.
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QDD27 - 06/03/2008
Fragala , I. ; Gazzola, F.
Partially overdetermined elliptic problems | Abstract | | We consider semilinear elliptic Dirichlet problems in bounded domains, overdetermined with a Neumann condition on a proper part of the boundary. Under different kinds of assumptions, we show that these problems admit a solution only if the domain is a ball. When these assumptions are not fulfilled, we discuss possible counterexamples to symmetry.
We also consider Neumann problems overdetermined with a Dirichlet condition on a proper part of the boundary, and the case of partially overdetermined problems on exterior domains.
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QDD26 - 04/03/2008
Barchielli, A.; Gregoratti, M.
Quantum continual measurements: the spectrum of the output | Abstract | | When a quantum system is monitored in continuous time, the result of the measurement is a stochastic process. When the output process is stationary, at least in the long run, the spectrum of the process can be introduced and its properties studied. A typical continual measurement for quantum optical systems is the so called homodyne detection. In this paper we show how the Heisenberg uncertainty relations give rise to characteristic bounds on the
possible homodyne spectra and we discuss how this is related to the typical quantum phenomenon
of squeezing. |
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QDD25 - 05/02/2008
Barchielli, A.; Gregoratti, M.; Licciardo, M.
Quantum trajectories, feedback and squeezing | Abstract | | Quantum trajectory theory is the best mathematical set up to model continual observations of a quantum system and feedback based on the observed output. Inside this framework, we study how to enhance the squeezing of the fluorescence light emitted by a two-level atom, stimulated by a coherent monochromatic laser. In the presence of a Wiseman-Milburn feedback scheme, based on the homodyne detection of a fraction of the emitted light, we analyze the squeezing dependence on the various control parameters. |
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