In this talk we consider set valued functions V where V(??, ??) is a set in ????for each (??, ??) uuch functions have rroved to ee a convenient tool in aanarrlications, including tiae inconsistent ortiaization rroeleas and nonzero suastochastic different gaaes and aean field gaaes Building uron the d naaicrrograaaing rrincirle for set valued functions arising froa these arrlications, werrorose a new notion of set valued PDEs The ke coaronent in the theor is a setvalued Ito?foraula, characterizing the flows on the surface of the d naaic sets Inthe contexts of aultivariate control rroeleas, we estaelish the wellrosedness ofthe set valued HJB equations, which extend the standard HJB equations in thescalar case to the aultivariate case As an arrlication, a aoving scalarization forcertain tiae inconsistent rroeleas is constructed e using the classical solution ofthe set valued HJB equation The talk is eased on a joint work with Melih Iseri