TY - JOUR
T1 - Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations
AU - Hieber, Matthias Georg
AU - Monniaux, Sylvie
PY - 2000
Y1 - 2000
N2 - In this paper, we show that a pseudo-differential operator associated to a symbol a ε L∞(ℝ × ℝ, L(H)) (H being a Hubert space) which admits a holomorphic extension to a suitable sector of ℂ acts as a bounded operator on L2(ℝ, H). By showing that maximal Lp-regularity for the nonautonomous parabolic equation u′(t)+A(t)u(t) = f(t), u(0) = 0 is independent of p ε (1, ∞), we obtain as a consequence a maximal Lp([0, T], H)-regularity result for solutions of the above equation.
AB - In this paper, we show that a pseudo-differential operator associated to a symbol a ε L∞(ℝ × ℝ, L(H)) (H being a Hubert space) which admits a holomorphic extension to a suitable sector of ℂ acts as a bounded operator on L2(ℝ, H). By showing that maximal Lp-regularity for the nonautonomous parabolic equation u′(t)+A(t)u(t) = f(t), u(0) = 0 is independent of p ε (1, ∞), we obtain as a consequence a maximal Lp([0, T], H)-regularity result for solutions of the above equation.
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M3 - Article
AN - SCOPUS:23044520222
VL - 128
SP - 1047
EP - 1053
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 4
ER -