Abstract Let Ω be a bounded convex open set of n , n ≥ 2, ∂Ω of class C^ 2. We consider the following Cauchy–Dirichlet problem where f L 2,λ(0, T; L 2(Ω, N )), 0 < λ < 1. F satisfies Campanato's Condition A x and is measurable on Ω × [0, T ]. We show that there exists ϵ that depends on the constants appearing in Condition A x such that for any μ (0, λ] with μ < ϵ, Moreover, if F is continuous on (x, t) then
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