We consider the following autonomous variational problem: minimize {\int_a^b f(v(x), v′(x))dx: v ∈ W^{1,1}(a, b), v(a) = α, v(b) = β} where the Lagrangian f is assumed to be continuous, but not necessarily coercive, nor convex. We show that the existence of the minimum is linked to the solvability of certain constrained variational problems. This allows us to derive existence theorems covering a wide class of nonconvex noncoercive problems.
Existence of minimizers of free autonomous variational problems via solvability of constrained ones / Cupini, G.; Guidorzi, M.; Marcelli, Cristina. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 26:4(2009), pp. 1183-1205.
Existence of minimizers of free autonomous variational problems via solvability of constrained ones
MARCELLI, Cristina
2009-01-01
Abstract
We consider the following autonomous variational problem: minimize {\int_a^b f(v(x), v′(x))dx: v ∈ W^{1,1}(a, b), v(a) = α, v(b) = β} where the Lagrangian f is assumed to be continuous, but not necessarily coercive, nor convex. We show that the existence of the minimum is linked to the solvability of certain constrained variational problems. This allows us to derive existence theorems covering a wide class of nonconvex noncoercive problems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.