1,720,983 research outputs found
On the closure of reachable sets for control systems.
No full textWe prove a density result related to control systems with closed reachable set
On minima of radially symmetric functionals of the gradient.
No full textIn this paper we consider the problems of the existence, the uniqueness and the qualitative properties (symmetry) of the minima to a minimization problem in the calculus of variations
On the validity of the maximum principle and of the Euler-Lagrange equation for a minimum problem depending on the gradient
No full textWe consider the limiting case alpha = infinity of the problem of minimizing integral(Omega) (\\del u(x)\\(alpha) + g(u))dx on u is an element of + u(0) + W-0(1, alpha) (Omega); where g is differentiable and strictly monotone. If this infimum is finite, it is evidently attained; we show that any minimizing function u satisfies the appropriate form of the Euler-Lagrange equation, i.e., for some function p, div p(x) = g'(u(x)) for p(x) is an element of partial derivative(jB)(del(x)); where j(B) is the indicator function of the closed unit ball in the Euclidean norm of R-N and partial derivative is the subdifferential of the convex function j(B)
Functions with prescribed singular values of the gradient.
No full textWe prove the existence of infinitely many vector-valued Lipschitz-continuous functions u on an open set Ω satisfying suitable Dirichlet boundary conditions such that the singular values of the gradient matrix ∇u, agree a.e. on Ω with N given positive, bounded and lower semicontinuous functions
On a problem of potential wells.
No full textWe find an explicit solution for a potential wells problem in dimension 3
A correction of the paper "On minima of radially symmetric functionals of the gradient"
No full textWe prove a theorem for the existence of solutions to a variational problem, under assumptions that do not require the convexity of the integrand
Nonconvex variational problems related to a hyperbolic equation
No full textWe first prove a new Lyapunov-type theorem which will yield existence of solutions to nonconvex minimum problems involving some hyperbolic equations on rectangular domains with Darboux boundary conditions. Some problems with obstacle and bang-bang results are also considered
Existence of solutions for a class of non convex minimum problems
No full textIn this paper we give sufficient conditions for the existence of solutions to the problem of minimizing the integral of [f ( ∇v) + v] on a convex n-dimensional set Ω . Here f is nonnegative, nonconvex, Borel-measurable, and vanishes on the boundary of a convex n-dimensional set K
Local Lipschitz continuity for energy integrals with slow growth and lower order terms
No full textWe consider integral functionals with slow growth and explicit dependence on of the Lagrangian; this includes many relevant examples as, for instance, in elastoplastic torsion problems or in image restoration problems. Our aim is to prove that the local minimizers are locally Lipschitz continuous. The proof makes use of recent results concerning the Bounded Slope Conditions
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