Existence Theorems for Multiple Integrals of the Calculus of Variations for Discontinuous Solutions (*).

Summary.- The authors prove existence theorems /or the minimum o] multiple integrals o / the calculus of variations with constraints on the derivatives in classes of BV possibly discon-tinuous solutions. To this eMeet he integrals are written in the]orm proposed by Serrin. Usual convexity conditions are requested, but no growth condition. Preliminary closure and semicontinuity heorems are proved which are analogous to those previously proved by Cesari in Sobolev classes. Compactness in.L 1 o] classes o] BV]unctions with equibounded total variations is derived #ore Ca]iero-~leming theorems. 1.- In t roduct ion. [ In the present paper we state and prove existence theorems of optimal solutions for multiple integrals of the calculus of variations, with constraints on the deriva-tives of the type =lEo(t, x(t), Dx(t)) dt, I (x)