Nonconvex Minimization Problems for Functionals Defined on Vector Valued Functions

AbstractWe consider the minimization problemminv∈W1,10(BnR,Rm)∫BnRf∇vx+hvxdx,where BnR is the ball of Rn centered at the origin and with radius R>0, f is a lower semicontinuous function, and h is a convex function. We give sufficient conditions for the existence and uniqueness of minimizers. Our technique relies on a detailed knowledge of the properties of the solutions to the convexified problem, obtained using the corresponding Euler–Lagrange inclusions