We show that local minimizers of functionals of the form ∫Ω[f(Du(x)) + g(x, u(x))] dx, u ∈0 + W 01,p(Ω), are locally Lipschitz continuous provided f is a convex function with p - q growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.

Existence and regularity of minimizers of nonconvex integrals with p-q growth / CELADA P; G. CUPINI; GUIDORZI M. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - STAMPA. - 13:(2007), pp. 343-358. [10.1051/cocv:2007014]

Existence and regularity of minimizers of nonconvex integrals with p-q growth

CUPINI, GIOVANNI;
2007

Abstract

We show that local minimizers of functionals of the form ∫Ω[f(Du(x)) + g(x, u(x))] dx, u ∈0 + W 01,p(Ω), are locally Lipschitz continuous provided f is a convex function with p - q growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.
13
343
358
CELADA P; G. CUPINI; GUIDORZI M
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/251221
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? ND
social impact