Regularity and uniqueness results in grand Sobolev spaces for parabolic equations with measure data

In this paper we prove some regularity and uniqueness results for a class of nonlinear parabolic problems whose prototypeis∂ₜ u - ΔN u=μ in D'(Q)u=0$ on $]0,T[×∂ (0)=u₀ in Ω,where Q is the cylinder Q=(0,T)×Ω, $T>0$,Ω⊂ Rⁿ, N≥ 2, isan open bounded set having C² boundary, μ¹(0,T;M(Ω))and u₀ belongs to M(Ω), the space of theRadon measures inΩ, or to L¹(Ω). The results are obtained in theframework of the so-calledgrand Sobolev spaces, and represent an extension ofearlier results onstandard Sobolev spaces.