TY - JOUR
T1 - R-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type
AU - Denk, Robert
AU - Hieber, Matthias Georg
AU - Prüss, Jan
PY - 2003/11
Y1 - 2003/11
N2 - The property of maximal Lp-regularity for parabolic evolution equations is investigated via the concept of R-sectorial operators and operator-valued Fourier multipliers. As application, we consider the L q-realization of an elliptic boundary value problem of order 2m with operator-valued coefficients subject to general boundary conditions. We show that there is maximal Lp-Lq-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.
AB - The property of maximal Lp-regularity for parabolic evolution equations is investigated via the concept of R-sectorial operators and operator-valued Fourier multipliers. As application, we consider the L q-realization of an elliptic boundary value problem of order 2m with operator-valued coefficients subject to general boundary conditions. We show that there is maximal Lp-Lq-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.
KW - Differential operators with operator-valued coefficients
KW - L-theory for boundary value problems of general type
KW - Lopatinskii-Shapiro condition
KW - Maximal L-regularity
KW - Operator-valued Fourier multipliers
KW - R-boundedness
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M3 - Article
AN - SCOPUS:0242287337
JO - Memoirs of the American Mathematical Society
JF - Memoirs of the American Mathematical Society
SN - 0065-9266
IS - 788
ER -