Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 868 products
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QDD129 - 07/23/2012
Cipriani F.; Sauvageot J.L.
Variations in Noncommutative Potential Theory: finite-energy states, potentials and multipliers | Abstract | | In this work we undertake an extension of various aspects of the potential theory of Dirichlet forms from locally compact spaces to noncommutative C-star-algebras with trace. In particular we introduce finite-energy states, potentials and multipliers of Dirichlet spaces. We prove several results among which the celebrated Deny s embedding theorem and the Deny s inequality, the fact that the carre du champ of bounded potentials are finite-energy functionals and the relative supply of multipliers. |
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QDD128 - 07/21/2012
Sesana, D.; Marazzina, D.; Fusai, G.
Pricing Exotic Derivatives Exploiting Structure | Abstract | | In this paper we introduce a new fast and accurate numerical method for pricing exotic derivatives when discrete monitoring is applied. The algorithm is general and is examined in detail with reference to the CEV (Constant Elasticity of Variance) process, for which up to date no efficient procedures are available. The approach exploits the structure of the matrix arising from the numerical quadrature of the pricing backward formulas to devise a convenient factorization that helps greatly in the speed-up of the recursion. The algorithm is applied to different exotic derivatives, such as Asian, barrier, Bermudan, lookback and step options. Extensive numerical experiments confirm the theoretical results.
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QDD127 - 07/12/2012
Gazzola, F.; Pavani, R.
Wide oscillations finite time blow up for solutions to nonlinear fourth order differential equations | Abstract | | We give sufficient conditions for local solutions to some fourth order semilinear ordinary differential equations to blow up in finite time with wide oscillations. This phenomenon is not visible for lower order equations. This result is then applied to several classes of semilinear partial differential equations in order to characterize the blow up of solutions. In particular, its applications to a suspension bridge model are widely discussed. We also give numerical results which describe this oscillating blow up and allow to suggest several open problems and formulate some related conjectures. |
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QDD126 - 07/11/2012
Gazzola, F.
On the moments of solutions to linear parabolic equations involving the biharmonic operator | Abstract | | We consider the solutions to Cauchy problems for the parabolic equation $u_ tau + Delta^2u=0$ in $ mathbb{R}_+ times mathbb{R}^n$, with fast decay initial data. We study the behavior of their moments. This enables us to give a more precise description of the sign-changing behavior of solutions corresponding to positive initial data. |
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QDD125 - 07/01/2012
Pagani, C.D.; Pierotti, D.
A three dimensional Steklov eigenvalue problem with exponential nonlinearity on the boundary | Abstract | | We investigate the existence of pairs (λ, u), with λ > 0 and u harmonic function in a bounded domain Ω ⊂ R3, such that the nonlinear boundary condition ∂u = λ μ sinh u holds on ∂Ω, where μ is a non negative weight function. This type of exponential boundary condition arises in corrosion modeling (Butler Volmer condition). |
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QDD124 - 06/27/2012
Bramanti, M.; Niu, P.; Zhu, M.
Interior HW^{1,p} estimates for divergence degenerate elliptic systems in Carnot groups | Abstract | | Let X_{1},…,X_{q} be the basis of the space of horizontal vector fields on a homogeneous Carnot group in R^n (q |
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QDD122 - 05/14/2012
Bonforte, M.; Grillo, G.; Vazquez, J.L.
Quantitative Local Bounds for Subcritical Semilinear Elliptic Equations | Abstract | | The purpose of this paper is to prove local upper and lower bounds for weak solutions of suitable classes of semilinear elliptic equations, defined on bounded Euclidean domains, without reference to the boundary behaviour. We give an explicit expression for all the involved constants. As a consequence, we obtain local Harnack inequalities with explicit constants, as well as gradient bounds. |
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QDD123 - 05/14/2012
Grillo, G.; Muratori, M.; Porzio, M.M.
Porous media equations with two weights: existence, uniqueness, smoothing and decay properties of energy solutions via Poincaré inequalities | Abstract | | We study weighted porous media equations on Euclidean domains, either with Dirichlet or with Neumann homogeneous boundary conditions. Existence of weak solutions and uniqueness in a suitable class is studied in detail. Moreover, short time smoothing effects in Lebesgue spaces are discussed for short time, in connection with the validity of a Poincaré inequality in appropriate weighted Sobolev spaces, and the long-time asymptotic behaviour is also studied. In fact, we prove full equivalence between certain smoothing effects and suitable weighted Poincaré-type inequalities. Particular emphasis is given to the Neumann problem, which is much less studied in the literature, as well as to the case of the whole Euclidean case when the corresponding weight makes its measure finite, so that solutions converge to their weighted average instead than to zero. Examples are given in terms of wide classes of weights. |
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