Tuesday, January 17, 2023 - 10:00 in ZOOM - Video Conference
A density result in with application to doubly nonlinear evolution equations in $L^1$
A talk in the Bielefeld Stochastic Afternoon series by
Daniel Hauer
| Abstract: |
Let $L^2$ be the classical Lebesgue space of square
integrable functions defined on a $\sigma$-finite measure space. If
$\mathcal{E}$ is a proper, convex and lower semi-continuous function
on $L^2$, then it is well-known (cf, Brezis [North-Holland Publ. Co.,
Amsterdam, 1973] or Barbu [Springer Monographs in Mathematics, 2010])
that the domain $D(\partial\mathcal{E})$ of the sub-differential
$\partial\mathcal{E} $ in $L^2$ is dense in the $L^2$-closure of the
effective domain $D(\mathcal{E})$ of $\mathcal{E}$. In this talk, I
present a generalization of this classical density result for the
composition operator $\partial\mathcal{E} \circ \phi$ in $L^1$, where
$\phi$ is a strictly monotone increasing function on $\mathbb{R}$. We
illustrate the usefulness of this density result on doubly nonlinear
evolution equations in $L^1_{\mu}$.
This is a joint work with my PhD student Timothy Collier (University of Sydney)
Within the CRC this talk is associated to the project(s): A5, B1 |
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