Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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On the continuity of the solution of the singular equation (β(u))_t=Lu
No full textWe extend some result of [2] proving the continuity of bounded solutions of the singular equation (β(u))_t=Lu where L is a more general operator of second order
A covariant and extended approach to some physical problems with constrained field variables
Get PDFMany physical problems are described by means of systems S of partial differential equations, whose field variables u are restricted by relations of the type Φ_I (u) = 0. Some examples, to this regard, are the ultrarelativistic gases studied in the framework of Extended Thermodynamics, the relativistic magnetofluiddynamics and the Maxwell Equations in the relativistic form. Here a general method is proposed to deal with problems of this kind; in particular, a new system S\u27 is proposed in the independent variables u, ψ R which are not restricted. Moreover, the solutions of S\u27 with �Φ_I (u) = 0, ψ_R =0, are the same of the original system S. The new system S\u27 is expressed inthe covariant form and is hyperbolic, under the assumption that the original system S satisfies these properties; Φ_I (u) = 0, ψ_R = 0 are satisfied as consequences of S\u27 and of the intial conditions. The new variables ψ_R are only auxiliary quantities
An extension of a theorem by M. I. Freidlin to good solutions to elliptic nondivergence equations
Get PDFIn the context of second order linear uniformly elliptic equations with measurable coefficients, a result of Freidlin [9], which deals with homogenization type properties for elliptic equations with smooth periodic coefficients, is extended to generalized solutions for equations with measurable coefficients
Convergence in generalized Schatten classes of operators
Get PDFIn this paper we give definitions for several generalized Schatten classes of operators and prove that several properties from the classes S_p can be generalized to them. The main goal is characterization of convergence in these classes. We also will prove that they are quasi-Banach spaces
Spherical-harmonic type expansion for the Boltzmann equation in semiconductor devices
Get PDFThe Boltzmann equation for an electron gas in a semiconductor is considered. The electron energy is assumed to have a very general form, so that, for instance, parabolic or non parabolic band approximations can be treated. A technique, which recalls the classical moment method due to Grad, to deduce an approximate quasi-hydrodynamical model is shown and compared with the spherical harmonic expansion. Some characteristics of the model, as entropy inequality, are explicitly presented
Theory of multivariable Bessel functions and elliptic modular functions
Get PDFThe theory of multivariable Bessel functions is exploited to establish further links with the elliptic functions. The starting point of the present investigations is the Fourier expansion of the theta functions, which is used to derive an analogous expansion for the Jacobi functions (sn,dn,cn...) in terms of multivariable Bessel functions, which play the role of Fourier coefficients. An important by product of the analysis is an unexpected link with the elliptic modular functions
An abstract ultraparabolic integrodifferential equation
Get PDFWe prove an existence and uniqueness result for a ultraparabolic integrodifferential equation in the strip [0, T1 ] × [0, T2 ] in the context of the spaces of continuous functions with values in a Banach space X and we give some applications to specific partial integrodifferential problems
