Sentence examples for existence of minimizers from inspiring English sources

In many variational problems, weak lower semicontinuity is an essential condition for the existence of minimizers, using the minimization method.

In this paper we develop a new method to prove the existence of minimizers for a class of constrained minimization problems on Hilbert spaces that are invariant under translations.

(assuming the existence of minimizers).

We prove the existence of minimizers using a relaxation technique.

To prove the existence of minimizers of I, another important point is requiring its coercivity condition.

Various conditions for the existence of minimizers of I have been greatly studied, see [9 21].

In this section, we present some properties of the functional F, and we prove the existence of minimizer.

This is the minimal framework to guarantee existence of the minimizers at each step, and to get estimates as in (2.11) providing the existence of a limit curve.

Given a p>2, we prove existence of global minimizers for a p-Ginzburg Landau-type energy over map-Ginzburg Landau-type="1 at infinity.

We are able to prove that the singular extremals of ((mathcal {P}_{S})) are normal, however, we are not able to establish a clear relationship between the number of switchings and the existence of abnormal minimizers as in [93].

These a priori estimates allow to prove that we have a Cauchy sequence, and then allow to get rid of the compactness part of the proof (by the way, we could even avoid using compactness so as to prove existence of a minimizer at every time step, using almost-minimizers and the in the Ekeland's variational principle [39]).