On lower perturbations of a class of non-convex integrals ^*

^*Part of this work has been presented at the International Congress of Mathematicians, held at Zurich in August, 1994. This was possible thanks to a grant awarded from the International Mathematical Union, to whom the author expresses his deep gratitude.

Abstract

Given h : R→R in a certain class of non-convex functions, we determine lower continuous perturbations to the (non-convex) integral of the Laplacian associated to h. This allows us to formulate a perturbed minimizing problem without any solution although the unperturbed problem always admits a solution. When some additional conditions on h are imposed the perturbation can be chosen as small as one may desire.

Keywords:

• A M S49 A 22

^*Part of this work has been presented at the International Congress of Mathematicians, held at Zurich in August, 1994. This was possible thanks to a grant awarded from the International Mathematical Union, to whom the author expresses his deep gratitude.

^*Part of this work has been presented at the International Congress of Mathematicians, held at Zurich in August, 1994. This was possible thanks to a grant awarded from the International Mathematical Union, to whom the author expresses his deep gratitude.

Notes

^*Part of this work has been presented at the International Congress of Mathematicians, held at Zurich in August, 1994. This was possible thanks to a grant awarded from the International Mathematical Union, to whom the author expresses his deep gratitude.