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Memoirs of the American Mathematical Society
2003; 114 pp; softcover
List Price: US$58
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Order Code: MEMO/166/788
The property of maximal \(L_p\)-regularity for parabolic evolution equations is investigated via the concept of \(\mathcal R\)-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 \(L_p\)-\(L_q\)-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.
Graduate students and research mathematicians interested in differential equations.
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