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Let $p \in (1,\infty)$. We are interested in strong $L^p$-solutions to the heat equation in $\mathbb{R}^n$. $$ \begin{cases} \partial_t u = \Delta u + f \\ u(0) = 0. \end{cases} $$ It is well-...

When investigaing the regularity of certain functions, I encountered this problem: if $u\in H^{3/2}([0,1]\times [0,1])$, what can we say about the continuity of $\nabla u\cdot\overrightarrow{n}$ ...