Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4200
 Title: Pointwise versions of solutions to Cauchy problems in $L^p$-spaces Authors: Desch, WolfgangHoman, Krista W. Issue Date: 2002 Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche Source: W. Desch and K. W. Homan, "Pointwise versions of solutions to Cauchy problems in $L^p$-spaces", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 34 (2002), pp. 121-142. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics34 (2002) Abstract: We consider a cauchy problem $\begin{array}{cc}\frac{\partial}{\partial t}\varphi\left(t,\omega\right)=\left(\mathcal{A\varphi\left(\mathit{t,\cdot}\right)}\right)\left(\omega\right),t>0 & \omega\epsilon\Omega\\\varphi\left(0,\omega\right)=\varphi_{0}\left(\omega\right), & \omega\epsilon\Omega\end{array}$ and assume that it can be solved by a strongly continuous semigroupon a Banach space valued function space $L^{p}\left(\Omega,X\right)$.For fixed t > 0 the solution $\varphi\left(t,\omega\right)$ is onlydefined almost everywhere on $\Omega$. Therefore it is not obviouswhat kind of regularity of $t\mapsto\varphi\left(t,\omega\right)$has for fixed $\omega\;\epsilon\;\Omega$. We show that if the semigroupis analityc, then there exists a version of $\varphi\left(t,\cdot\right)$such that for almost every $\omega\;\epsilon\;\Omega$, $t\mapsto\varphi\left(t,\omega\right)$is analityc in $\left(0,\infty\right)$. Type: Article URI: http://hdl.handle.net/10077/4200 ISSN: 0049-4704 Appears in Collections: Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.34 (2002)

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