Partial regularity for the solutions to nonlinear parabolic systems

Sunto Si estendono a sistemi non lineari di tipo parabolico alcuni risultati di regolarità parziale delle soluzioni di sistemi ellittici.

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Entrata in Redazione il 19 settembre 1972.

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Research supported in part by a C.N.R. fellowship at the University of Paris.

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Research partially supported by NSF Grant GP 16115.     

A ecessary and Sufficient Condition for The Stability of General molecular Systems

We study here the binding of atoms and molecules and the stability of general molecular systems including molecular ions. This is the first paper of a series devoted to the study of these general problems. We obtain here a general necessary and sufficient condition for the stability of general molecular ststem in the context of thomasz-Fermi-Von Weiasäcker, Thomas-Fermi-Dirac-Von Weizsaäcker, Hartree or Hartree-Fock theories

SUMARY OF PART 1

1.Introduction.

II.Presentation of the models

III.Diatomic molecular systems and hartree-Fock theory

IV.Diatomic molecular systems and Hartree or Thomas-Fermi theories

V.General molecular systems

Appendix 1: Hartree-Fock models when Z > N ― 1

Appendix 2: Dichotomy yields equal Lagrange multipliers

Appendix 3: The problem at infinty for the TRDW model     

Stratifications distinguées comme outil en géométrie semi-analytique

We introduce the distinguish stratifications as a new tool in order to give new proofs of some essential facts in the semi-analytic geometry in an easier way, for example the property of regular separation.

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Partially supported by KBN grant PB 1219/2/91

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Partially supported by KBN grant PB 1219/2/91

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Partially supported by DGICYT.     

A characterization of the entropy functionals for grand canonical ensembles. The discrete case

Summary ? Natural ? properties lead to a representation theorem for the entropy functional of a grand canonical ensemble. In addition to the classical Boltzmann term, the representation contains three more terms that seem to be meaningful in statistical mechanics.

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Sunto Da proprietà ? naturali ? imposte al funzionale entropia di un insieme gran canonico si deduce un teorema di rappresentazione per esso. In aggiunta al termine classico di Boltzmann, la rappresentazione mette in luce tre ulteriori termini che sembrano significativi in meccanica statistica.

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A Dario Graffi per il suo 70° compleanno

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Entrata in Redazione il 17 marzo 1976.

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While on sabbatical leave of absence from the University of Waterloo, Canada, Department of Applied Mathematics.

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Research supported in part by National Research Council of Canada, grant A-7677 and IBM-Italia.     

Alcune soluzioni esatte delle equazioni della magnetofluidodinamica per il moto stazionario di un fluido viscoso,incomprimibile e a conducibilità elettrica finita

Summary With regard to the non-linear equations of Magneto-Fluid Dynamics in this paper we examine the steady, axially symmetric motion of an incompressible, homogeneous, viscous and electrically conducting fluid when such a fluid moves also around the axis of symmetry. We give some classes of exact solutions and then we generalize the problem taking also in account the Hall effect.

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A Dario Graffi nel suo 70^o compleanno

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Entrata in Redazione il 23 gennaio 1975.

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Istituto Matematico dell'Università di Siena.     

Superfici di curvatura media assegnata con ostacolo

Summary In this paper we demonstrate the existence and the regularity of surfaces of prescribed mean curvature with Lipschitz-continuous obstacles.

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Entrata in Redazione il 13 giugno 1975.

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Lavoro svolto nell'ambito del GNAFA-CNR.     

On the Absence of a First Order COrrection for the Number of Bound States of a Schrödinger operator with Coulomb Singularity

Contents

1 Introduction 616

2 Regularizaton of the Singular Operator 620

3 Functional Calculus with Projections 621

A The Kutaanheimo–Stiefel Transform and All That 625

B Some Remarks on a Result of Petkov and Robert on the Counting Function in the Context of Compact Group Actions 627

B.1 Introduction and Principal Statements 627

B.2 Sketch of a Proof of Theorem 10 632

B.3 On the Initial Conditions Yielding Periodic Orbits of Regularized and Unregularized Hamiltonians 634

B.4 On the Vanishing of the Second Coefficient 635     

Sulla stabilità asintotica parziale

Summary In this paper the well known theorems of E.A. Barbaschin-N.N. Krasovskij and J. P. LaSalle on asymptotic statility and instability are extended to partial stability. An application is given for a class of non-holonomic dissipative mechanical systems.

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A Bruno Finzi nel suo70 ^mo compleanno.

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Lavoro svolto nell'ambito dei Gruppi di Ricerca del Comitato per la Matematica del C.N.R.

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Entrata in Redazione il 23 marzo 1970.     

Parametrized\bar \partial operator on pseudoconvex setsoperator on pseudoconvex sets

Sunto Si dimostra l'esistenza della soluzione per l'operatore di Cauchy-Riemann parametrizzato, nel caso continuo per varietà fortemente pseudoconvesse e nel caso differenziabile per varietà di Stein.

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Entrata in Redazione il 20 maggio 1975.

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Supported by C.N.R. research groups.     

Sul teorema di Riesz-Thorin

Summary We give an extension of the Riesz-Thorin theorem to linear operators which map Morrey spaces in spaces of the same or similar type.

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A Bruno Finzi nel suo 70^mo compleann

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Entrata in Redazione il 10 dicembre 1969.     

Sur la régularité des solutions de l'équation divA(x,u, ∇u)=B(x,u, ∇u) avec des conditions aux limites unilatérales et mêlées

Sunto. In questo lavoro dimostreremo la regolarità L^p, L^∞ e h?lderiana delle soluzioni di una classe di equazioni differenziali non lineari di tipo ellittico soggette a condizioni di frontiera di tipo misto e unilaterale

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Thèse presentée à la Faculté des Sciences de Paris le 2 juin 1971.

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Boursier de le ? Instituto de Alta Cultura ? (Portugal).

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Entrata in Redazione il 28 giugno 1971.     

Esistenza ed unicità delle soluzioni di una classe di problemi ipoellittici

Summary In this paper are studied existence and unicity of solutions of a class of hypoelliptic problems.

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Entrata in Redazione il 20 novembre 1974.

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Lavoro eseguito nell'ambito del Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni del C.N.R.     

The Existence Of Nonhomogeneous,Viscous And Incompressible Flow In Unbounded Domains

The existence of global (in time) solution {ρu,p} (density, velocity field and pressure) of a partial differential problem modelling the behaviour of a viscous, nonhomogenous and incompressible flow has been recently obtained viscous, nonhomogenous and incompressible flow has been recently obtained by J. Simon. In his most general result, he finds a solution which satifies an initial condition in an appropriate weak sense. In this paper, we present an extension of this result to the case of arbitrary unbounded three–dimensional fluid domains.

1. Introduction.

2. The main result.

3. Some technical Lemmas.

4. Proof of Theorem 1.

4.1 The existence and properties of {ρR, U^R PR}

4.2 Some estimates for ρR,U^R and their time derivatives.

4.3 Further estimates.

4.4 The choice of a convergent sequence and conclusions.

References.     

Equazioni ellittiche del secondo ordine di tipo Cordes con termini di ordine inferiore

Summary I study the spectrum of linear second order elliptic partial differentiat equations of Cordes type with lower order terms.

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Lavoro eseguito nell'ambito dell'attività dei gruppi di ricerca matematica del Consiglio Nazionale delle Ricerche.

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Entrata in Redazione il 26 ottobre 1969.     

Geometrische Beziehungen in der Aerodynamik kompressibler Medien

There are investigated and discussed relations between the stream-function-surface and the pressure-surface in the theory of the two-dimensional isentropic steady flow in gasdynamics.

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A Bruno Finzi nel suo 70^mo compleanno.

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Entrata in Redazione il 19 gennaio 1970.     

Punti esplosivi (radianti o vibranti) delle equazioni differenziali ordinarie del 2o ordine

Summary It is given in § 1.

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All'amicoDario Graffi nel suo 70^o compleanno

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Entrata in Redazione il 3 aprile 1975.     

Una maggiorazione a priori dal punto di vista variazionale

Summary A class of linear second order ordinary differential operators is considered, with bounded measurable coefficients. An optimal a priori estimate for such operators is determined, using variational techniques.

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Entrata in Redazione il 12 febbraio 1975.

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Lavoro eseguito nell'ambito del G.N.A.F.A. del C.N.R.     

Spectral approximation of Wiener-Hopf operators with almost periodic generating function

The paper deals with spectral approximation of Wiener-Hopf operators acting on L^p -spaces by their

finite sections. The generating functions of the Wiener-Hopf operators are supposed to be continuous plus almost

periodic.While the usual spectra of the finite sections drastically fail to converge to the spectrum of the Wiener-Hopf

operator,it turns out that other spectral approximants, viz. the pseudospectra and the numerical ranges, do converge

perfectly.The proof requires a modified approach to the finite section method for Wiener-Hopf operators. This note

generalizes results obtained by Böttcher, Grudsky and Silbermann for the case of continuous generating

functions.     

Relations between generalized Koszul complexes

Sunto Si studiano le relazioni fra i complessi generalizzati di Koszul K(A; E; t), K(B; E; t) di R-moduli introdotti nel [4] che derifano da relazioni varie fra le matrici A, B.

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A BeniaminoSegre nel suo 70-mo compleanno.

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Entrata in Redazione il 9 marzo 1973.     

Sulla propagazione delle onde elettromagnetiche nei mezzi di Toupin e Rivlin

Summary The propagation of an ordinary plane wave in a medium of Toupin and Rivlin is here considered, limitedly to the instances of an external electric or magnetic field acting on the medium. In particular, the conditions for the propagation of T.E. and T.M. or T.E.M. waves are determined.

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A Dario Graffi nel suo 70^o compleanno

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Entrata in Redazione il 4 giugno 1976.

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Lavoro eseguito nell'ambito dei gruppi di ricerca del C.N.R. per la Fisica Matematica.