Abstract: In this work we study the regularity of entropy solutions of the genuinely nonlinear scalar balance laws

D_tu(x,t)+D_x[f(u(x,t),x,t)]+g(u(x,t),x,t)=0      in an open set Ω⊂R².

We assume that the source term g∈C¹(R×R×R⁺), that the flux function f∈C²(R×R×R⁺) and that {u_i∈R: f_uu(u_i,x,t)=0} is at most countable for every fixed (x,t)∈Ω. Our main result, which is a unification of two proposed intermediate theorems, states that BV entropy solutions of such equations belong to SBV_loc(Ω). Moreover, using the theory of generalized characteristics we prove that for entropy solutions of balance laws with convex flux function, there exists a constant C>0 such that:

u([x+h]+,t)−u(x−,t)≤Ch,    (h>0)

where C can be chosen uniformly for (x+h,t), (x,t) in any compact subset of Ω.