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8 votes

Maximal Hausdorff dimension of the set on which derivatives do not agree

I think the paper "A singular function with a non-zero finite derivative on a dense set with Hausdorff dimension one" answers exactly this question.
an_ordinary_mathematician's user avatar
4 votes

Dimension of the graph of a function $\varphi : \mathbb R^2 \to \mathbb R$

I don't believe it necessary that the dimension of the graph of $\varphi$ be larger than 2. An example is provided by examining Poisson's integral formula for the upper half plane: $$ u(x,y) = \frac{...
Mark McClure's user avatar
  • 1,963
1 vote

Dimension of the graph of a function $\varphi : \mathbb R^2 \to \mathbb R$

This answer is not complete (I am not sure that the function below is smooth). It seems $\dim_{\mathbb{H}} G(\varphi)$ may be exactly $2$. Let $f:\mathbb{R}\to\mathbb{R}$ be any continuous function, ...
Saúl RM's user avatar
  • 8,741

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