Linear parabolic problems induce isomorphisms in Sobolev spaces of generalized smoothness and yield necessary and sufficient conditions for the generalized regularity of solutions and their partial derivatives.
Lunardi.Analytic semigroups and optimal regularity in parabolic problems[2013 reprint of 1995 orig- inal],Modern Birkh¨ auser Classic
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Matrix parabolic problems in Sobolev spaces of generalized smoothness
Linear parabolic problems induce isomorphisms in Sobolev spaces of generalized smoothness and yield necessary and sufficient conditions for the generalized regularity of solutions and their partial derivatives.