On the existence and uniqueness of minimizers for a class of integral functionals

摘要

We study the solvability of the minimization problem min_(η∈Κ_α)∫ from x=0 to x=T of α(t)[f(|η'(t)|) + g(η(t))]dt, where Κ_α is a subset of ACloc[0, T] depending on the weight function α. Neither the convexity nor the superlinearity of f are required. The main application concerns the existence and uniqueness of minimizers to integral functionals on convex domains defined in the class of functions in depending only on the distance from the boundary of Ω. As a corollary, when Ω is a ball we obtain the existence of radially symmetric solutions to nonconvex and noncoercive functionals.