We consider variational problems whose lagrangian is of the form f(Du)+g(u) where f is a possibly non-convex lower semicontinuous function with p-growth at infinity for some 1 < p < ∞, and the boundary datum is any function in W 1,p (Ω). Assuming that the convex envelope of f is affine on each connected component of the set {f ^∗∗ < f }, we prove the existence of solutions to (P) for every continuous function g such that (i) g has no strict local minima and (ii) every convergent sequence of extremum points of g eventually belongs to an interval where g is constant, thus showing that the set of continuous functions g that yield existence to (P) is dense in the space of continuous functions on R.
Minimizing non-convex multiple integrals: a density result / P., Celada; Perrotta, Stefania. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - STAMPA. - 130(2000), pp. 721-741.
Data di pubblicazione: | 2000 |
Titolo: | Minimizing non-convex multiple integrals: a density result. |
Autore/i: | P., Celada; Perrotta, Stefania |
Autore/i UNIMORE: | |
Rivista: | |
Volume: | 130 |
Pagina iniziale: | 721 |
Pagina finale: | 741 |
Codice identificativo ISI: | WOS:000088977100003 |
Codice identificativo Scopus: | 2-s2.0-23044520958 |
Citazione: | Minimizing non-convex multiple integrals: a density result / P., Celada; Perrotta, Stefania. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - STAMPA. - 130(2000), pp. 721-741. |
Tipologia | Articolo su rivista |
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