$u$ is a function in $W^{1,p}(\Omega)$ for $1\le p \le +\infty$, and its first derivative $\partial u/\partial x^i$ is in $C(\Omega)$( the space of continuous functions on open set(a domain) $\Omega$), then how to show $u$ is in $C^1(\Omega)$?
2026-03-27 04:17:39.1774585059
How to show the smoothness of a function in sobolev space by using smoothness of its derivative?
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