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Displaying similar documents to “Structural discontinuities to approximate some optimization problems with a nonmonotone impulsive character”

On motions with bursting characters for Lagrangian mechanical systems with a scalar control. I. Existence of a wide class of Lagrangian systems capable of motions with bursting characters

Aldo Bressan, Marco Favretti (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this Note (which will be followed by a second) we consider a Lagrangian system Σ (possibly without any Lagrangian function) referred to N + 1 coordinates q 1 , q N , u , with u to be used as a control, and precisely to add to Σ a frictionless constraint of the type u = u t . Let Σ 's (frictionless) constraints be represented by the manifold V t generally moving in Hertz's space. We also consider an instant d (to be used for certain limit discontinuity-properties), a point q ¯ , u ¯ of V d , a value p ¯ for Σ 's momentum...

On the application of control theory to certain problems for Lagrangian systems, and hyper-impulsive motion for these. I. Some general mathematical considerations on controllizable parameters

Aldo Bressan (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In applying control (or feedback) theory to (mechanic) Lagrangian systems, so far forces have been generally used as values of the control u ( ) . However these values are those of a Lagrangian co-ordinate in various interesting problems with a scalar control u = u ( ) , where this control is carried out physically by adding some frictionless constraints. This pushed the author to consider a typical Lagrangian system Σ , referred to a system χ of Lagrangian co-ordinates, and to try and write some handy...

On the eigenvalues of an elliptic operator a x , H u

Sergio Campanato (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let Ω be a bounded open convex set of class C 2 . Let a x , H u be a non linear operator satisfying the condition (A) (elliptic) with constants α , γ , δ . We prove that a number λ 0 is an eigenvalue for the operator a x , H u if and only if the number α λ is an eigen-value for the operator Δ u . If λ 0 , the two systems a x , H u = λ u and Δ u = α λ u have the same solutions. In particular, also the eventual eigen-values of the operator a x , H u should all be negative. Finally, we obtain a sufficient condition for the existence of solutions u H 2 H 0 1 Ω ...

A propagation theorem for a class of microfunctions

Andrea D'Agnolo, Giuseppe Zampieri (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let A be a closed set of M R n , whose conormai cones x + y x * A , x A , have locally empty intersection. We first show in §1 that dist x , A , x M A is a C 1 function. We then represent the n microfunctions of C A | X , X C n , using cohomology groups of O X of degree 1. By the results of § 1-3, we are able to prove in §4 that the sections of C A | X π ˙ - 1 x 0 , x 0 A , satisfy the principle of the analytic continuation in the complex integral manifolds of H ϕ i C i = 1 , , m , ϕ i being a base for the linear hull of γ x 0 * A in T x 0 * M ; in particular we get Γ A × M T * M X C A | X A × M T ˙ * M X = 0 . When A is a half space with...

Persistence of Coron’s solution in nearly critical problems

Monica Musso, Angela Pistoia (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider the problem - Δ u = u N + 2 N - 2 + λ in Ω ε ω , u > 0 in Ω ε ω , u = 0 on Ω ε ω , where Ω and ω are smooth bounded domains in N , N 3 , ε > 0 and λ . We prove that if the size of the hole ε goes to zero and if, simultaneously, the parameter λ goes to zero at the appropriate rate, then the problem has a solution which blows up at the origin.

Γ -convergence of discrete approximations to interfaces with prescribed mean curvature

Giovanni Bellettini, Maurizio Paolini, Claudio Verdi (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The numerical approximation of the minimum problem: min A Ω F ~ A , is considered, where F ~ A = P Ω A + cos θ H n - 1 A Ω - A κ . The solution to this problem is a set A Ω R n with prescribed mean curvature κ and contact angle θ at the intersection of A with Ω . The functional F ~ is first relaxed with a sequence of nonconvex functionals defined in H 1 Ω which, in turn, are discretized by finite elements. The Γ -convergence of the discrete functionals to F ~ as well as the compactness of any sequence of discrete absolute minimizers are proven. ...