... ukk≤ ε ϕεon D and so 0 ≤ u1≤ ε ϕεon D. Thereby, the continuity of ϕε in every dense point of the boundary of D and the arbitrariness of ε guarantee thatu1∈ C0D.Finally, we will ... bT, v1H>Rand Φ1v1 < 0 and hence, since Φ100, by denoting as Γ1theclass of paths in H1joining 0 and v1, it follows from 3.16 thatc1: infγ∈Γ1maxv∈γ0,1Φ1v ... study of gas dynamics and fluids mechanics, and in the study of relativisticmechanics, nuclear physics, and chemically reacting system see, e.g., 1 and the referencestherein for the continuous...