We consider the functional F(v) = \int_a^b f(t,v′(t))dt in Hp = {v ∈ W^{1,p} : v(a) = 0, v(b) = d}, p ∈ [1, +∞]. Under only the assumption that the integrand is L ⊗ B_n-measurable, we prove characterizations of strong and weak minimizers both in terms of the minimizers of the relaxed functional and by means of the Euler–Lagrange inclusion. As an application, we provide necessary and sufficient conditions for the existence of the minimum, expressed in terms of a limitation on the width of the slope d.
Variational problems with nonconvex, noncoercive, highly discontinuous integrands: characterization and existence of minimizers / Marcelli, Cristina. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - STAMPA. - 40:5(2002), pp. 1473-1490.
Variational problems with nonconvex, noncoercive, highly discontinuous integrands: characterization and existence of minimizers
MARCELLI, Cristina
2002-01-01
Abstract
We consider the functional F(v) = \int_a^b f(t,v′(t))dt in Hp = {v ∈ W^{1,p} : v(a) = 0, v(b) = d}, p ∈ [1, +∞]. Under only the assumption that the integrand is L ⊗ B_n-measurable, we prove characterizations of strong and weak minimizers both in terms of the minimizers of the relaxed functional and by means of the Euler–Lagrange inclusion. As an application, we provide necessary and sufficient conditions for the existence of the minimum, expressed in terms of a limitation on the width of the slope d.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.