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 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.
AB - 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.
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:0346056028
SN - 0218-2165
VL - 6
SP - 467
EP - 481
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
IS - 5
ER -