2 problems

Let $(T_t)_{t\geqslant 0}$ be a weak continuous semigroup of selfadjoint contractive operators on $\mathrm{L}^\infty(\Omega)$, where $\Omega$ is a measure space. A Banach space $X$…

Let $\Omega$ be a two-dimensional bounded Lipschitz domain, and let $\mathrm{L}^p_{\sigma}(\Omega)$ denote the space of solenoidal vector fields in $\mathrm{L}^p(\Omega)$. Let $p$…