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Let A be a closed operator on a Banach space X . We study maximal L p -regularity of the problems $$ \begin{aligned} u^{\prime} (t) & = Au(t) + f(t)\quad {\hbox{and}}\\ u^{\prime\prime}(t) & = Au(t) + f(t) \end{aligned} $$ on the line. The results are used to solve quasilinear parabolic and elliptic problems on the line.
Journal of Evolution Equations – Springer Journals
Published: Dec 1, 2006
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