1,721,031 research outputs found
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)
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
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
On a problem of potential wells.
No full textWe find an explicit solution for a potential wells problem in dimension 3
On the existence of solutions to a class of minimum time control problems and applications to Fermat's Principle and to the Brachystocrone
No full textWe prove a theorem for the existence of solutions to minimum time control problems,
under assumptions that do not require the convexity of the images and that weaken the assumption of upper semicontinuity.
Our result applies to Fermat's principle and to the Brachystocrone
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