Un complemento del lavoro : «Questioni di esistenza e di unicità per il problema elastostatico con un vincolo di appoggio unilaterale a supporto rigido nel caso di piccole deformazioni»
Teoremi di esistenza e unicità in elastostatica finita
Questioni di esistenza e di unicità per il problema elastostatico con un vincolo di appoggio unilaterale a supporto rigido nel caso di piccole deformazioni
Qualche proprietà dei sistemi di vettori applicati possibili applicazioni alla teoria matematica dell'elasticità
Factorization of mappings and general existence theorems in locally convex spaces
A property of multiplication in Sobolev spaces. Some applications
Qualche proprieta e applicazione di sistemi di vettori definiti su una superficie
Proprietà dello stress minimizzante l'energia potenziale elastica in un insieme di stress «staticamente ammissibili»
On the notion of potential for mappings between linear spaces. A generalized version of the Poincaré lemma
An approach to the theory of linear differential forms in a radial subset of an (arbitrary) real linear space without a Banach structure is proposed. Only intrinsic (partially linear) topologies on are (implicitly) involved in the definitions and statements. Then a mapping , with , real linear spaces and a radial subset of , is considered. After showing a representation theorem of those bilinear forms on for which , we observe that the assignment...
A perturbation problem in the presence of affine symmetries
An approach to a local analysis of solutions of a perturbation problem is proposed when the unperturbed operator has affine symmetries. The main result is a local theorem on existence, uniqueness, and analytic dependence on a parameter.
Sulla formulazione variazionale - espressa nello stress - del problema dell'equilibrio dei corpi elastici con un vincolo eli appoggio unilaterale liscio. Nota II
We study the analytical problems connected with a variational formulation-expressed in terms of the stress-of the elastostatic problem when an unilateral supporting constraint without friction is present. Such a formulation is compared with a variational one expressed in terms of the displacement. This Nota II is the second section of the paper; the first section appears in Nota I, issue n. 5 of this volume.
Sulla formulazione variazionale - espressa nello stress - del problema dell'equilibrio dei corpi elastici con un vincolo di appoggio unilaterale liscio. Nota I
We study the analytical problems connected with a variational formulation—expressed in terms of the stress—of the elastostatic problem when an unilateral supporting constraint without friction is present. Such a formulation is compared with a variational formulation expressed in terms of the displacement. This Nota I is the first section of the paper; the second section will appear in Nota II, fasc. n. 6, of this volume.
Su un principio generale di esistenza in analisi lineare
In §1 we show that the well-known "Fichera existence principle in Banach spaces" (See [3], pp. 174-178; [2], [4], pp. 30-50; [5], pp. 11-16) holds—suitably enonciated-in locally convex Hausdorff spaces: the (very simple) proof is founded on the remark that the existence problem is equivalent to a property of inclusion of dual spaces. In §2 we explain how this principle includes, as particular cases, the so-called "Theorem of surjection of Fréchet spaces" (see [7], Theor. 37.2) and a generalisation...
Sulla differenziabilità dell'operatore di Nemytsky
The main result of this paper is a non-differentiability Theorem (Theorem 1) for a superposition operator, i.e. the Nemytsky operator. Two more differentiability theorems are proved (Theorems 2 and 3). The paper “Osservazioni sulla linearizzazione di un operatore differenziale” (following the present one in these “Rendiconti”) contains some consequences of Theorems 1, 2, 3 concerning certain problems connected with the study of a special class of nonlinear differential operators.
Osservazioni sulla linearizzazione di un operatore differenziale
In order to obtain some theorems of local existence and uniqueness for a non-linear differential problem and investigate about the significance of its linearization, we study the differentiability of a non-linear operator acting among Banach spaces for which the (formally) linearized operator is an isomorphism. We give a definition of “admissible linearization” with respect to a pair of Banach spaces. We consider a differential operator of the form , [where is the gradient of and is the...
An abstract setting for boundary problems with affine symmetries
Two symmetries of affine type for any mapping acting between Banach spaces are described and studied. These symmetries translate certain structural properties of boundary value problems for differential operators to an abstract setting.
Sulla forma integrale delle condizioni di congruenza per le deformazioni di un sistema continuo
We point out in which cases an integral condition on the (which has, for , an interesting mechanical meaning) can be interpreted as a sufficient condition for the existence of solutions of the set of partial differential equations , , where , being a bounded connected open set of . Furthermore, we show how this condition allows an integral (weak) formulation of the elastic equilibrium problem, when the stress is taken as principal unknown instead of the displacement.
Una decomposìzioue di uno spazio hilbertiano avente interesse e significato in Meccanica
Let be a measure on and let be a bounded measurable subset of finite measure of . We denote by the Hilbert space of all -valued functions square-integrable on with respect to , where the scalar product is defined as the integral over of the ordinary product of two vectors. We show that is the topological direct sum of two ortogonal subspaces, which have an evident mechanical meaning for . We show then some consequences and applications of the preceding result.
Sulla differenziabilità di un operatore legato a una classe di sistemi differenziali quasi-lineari
Local Existence of Solutions for Perturbation Problems with Non Linear Symmetries
The existence of local families of solutions for perturbation equations is proved when the free operator is covariant under a non linear action of a Lie group.
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