Maximal regularity for evolution equations in weighted Lp-spaces

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On quasilinear parabolic evolution equations in weighted Lp-spaces (2009, methodology): “ere we follow the approach based on Lp-maximal regularity. This approach was ﬁrst introduced in the paper by Cl´ement and Li [9] and has been further developed in [17, 23, 25]. Following the ideas in [26], this approach has recently been extended to weighted Lp-spaces in [17] for several reasons. Ti”
Traces and embeddings of anisotropic function spaces (2012, unknown): “Indeed, in many cases maximal regularity properties of parabolic problems are independent of the weight (see [28, 33]).”
Sharp embedding results for spaces of smooth functions with power weights (2011, methodology): “oeﬃcients or domains with a nonsmooth geometry (see e.g. [4, 22, 26, 42]). For evolution equations, power weights in time play an important role in order to obtain results for rough initial data (see [11, 20, 25, 31]). In addition, here one is naturally confronted with vector-valued spaces. Our work”
On quasilinear parabolic evolution equations in weighted Lp-spaces II (2009, background): “[11]. Concerning nontrivial initial data, it was shown in [ 21, Theorem 3.2 ] that if A0 2 MRp(X1,X0), then the initial value problem”