In a 2D domain, are the functions whose partial derivatives are simple functions dense in $W^{1,\infty}$ ?
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$\begingroup$ To provide context, the answer is yes in one dimension and false in any dimension if "functions whose partial derivatives are simple functions" is replaced with "piecewise linear functions". See this question: mathoverflow.net/q/212458/55893 $\endgroup$– Joonas IlmavirtaCommented Jul 28, 2015 at 9:56
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