Tent space well-posedness for parabolic Cauchy problems with rough coefficients

On regularity of weak solutions to linear parabolic systems with measurable coefficients

“…Uniqueness of pathwise weak solutions in L p (Ω; Ṫ p 1 ) is a key feature of our result, as the uniqueness problem is far from trivial in this context (as opposed to the context of mild solutions). We exploit for this the uniqueness result for deterministic equations in our earlier work with Monniaux [12] when p = 2, followed by its extension to general p by Zatoń [56].…”

Note on time-regularity for weak solutions to parabolic systems of 𝑝-Laplace type

“…We close this introduction with a brief comparison to our previous work with P. Auscher in [2], where we obtained regularity as in Theorem 2 for linear operators and p " 2 by a more involved approach. See also [9] for a generalization to higher order systems. The flexibility in the definition of the structure functions A and B, allows us to use Theorem 2 for inhomogenous linear systems of the form…”

Note on time-regularity for weak solutions to parabolic systems of p-Laplace type

“…We close this introduction with a brief comparison to our previous work with P. Auscher in [2], where we obtained regularity as in Theorem 2 for linear operators and p " 2 by a more involved approach. See also [9] for a generalization to higher order systems. The flexibility in the definition of the structure functions A and B, allows us to use Theorem 2 for inhomogenous linear systems of the form Bu i Bt ´div A i pt, x, ∇uq ´Bi pt, x, ∇uq " div F i `fi , i " 1, .…”