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The authors prove existence theorems for the minimum of multiple integrals of the calculus of variations with constraints on the derivatives in classes of BV possibly discontinuous solutions. To this effect the integrals are written in the form proposed by Serrin. Usual convexity conditions are requested, but no growth condition. Preliminary closure and semicontinuity theorems are proved which are analogous to those previously proved by Cesari in Sobolev classes. Compactness in L 1 of classes of BV functions with equibounded total variations is derived from Cafiero-Fleming theorems

Existence theorems for multiple integrals of the calculus of variations for discontinuous solutions