Heat-kernels and maximal Lp − Lq−estimates: the non-autonomous case
Résumé
In this paper, we establish maximal Lp−Lq estimates for non autonomous parabolic equations of the type u′(t) + A(t)u(t) = f(t), u(0) = 0 under suitable conditions on the kernels of the semigroups generated by the operators −A(t), t ∈ [0; T]. We apply this result on semilinear problems of the form u′(t) + A(t)u(t) = f(t; u(t)), u(0) = 0.
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