Minimizers That Are Not Also Relaxed Minimizers

Minimizers and symmetric minimizers for problems with critical Sobolev exponent

In this paper we will be concerned with the existence and non-existence of constrained minimizers in Sobolev spaces D(R ), where the constraint involves the critical Sobolev exponent. Minimizing sequences are not, in general, relatively compact for the embedding D(R) →֒ L ∗ (R , Q) when Q is a non-negative, continuous, bounded function. However if Q has certain symmetry properties then all minim...

A comparison principle for minimizers

We give some conditions that ensure the validity of a Comparison principle for the minimizers of integral functionals, without assuming the validity of the Euler–Lagrange equation. We deduce a weak maximum principle for (possibly) degenerate elliptic equations and, together with a generalization of the bounded slope condition, the Lipschitz continuity of minimizers. To prove the main theorem we...

Partial regularity for quasi minimizers

Exact Minimizers in Real Interpolation

We present some extensions of results presented in our recent papers. First we extend the characterization of optimal decompositions for a Banach couple to optimal decompositions for a Banach triple. Next we show that our approach can apply when complex spaces are considered instead of real spaces. Finally we compare the performance of the algorithm that we have proposed for the ROF model with ...

Continuity results for TV -minimizers

This paper deals with continuity preservation when minimizing generalized total variation with a L fidelity term or a Dirichlet boundary condition. We extend several recent results for these two types of data terms, mainly by showing comparison principles for the prescribed mean curvature problem satisfied by the level-sets of such minimizers. MSC2010: 49N60, 53A10, 94A08.