TY - JOUR
T1 - Heat-kernels and maximal Lp - Lq estimates
T2 - The non-autonomous case
AU - Hieber, Matthias Georg
AU - Monniaux, Sylvie
PY - 2000
Y1 - 2000
N2 - In this paper, we establish maximal Lp-Lq estimates for rum-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.
AB - In this paper, we establish maximal Lp-Lq estimates for rum-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.
KW - Heat-kernel estimates
KW - Maximal L - L- Regularity
KW - Non-autonomous cauchy problem
KW - Singular integrals
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M3 - Article
AN - SCOPUS:34247392750
SN - 1069-5869
VL - 6
SP - 467
EP - 481
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
IS - 5
ER -