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What is happening here : $\partial U $ is flat and $x^o \in \partial U $ is the center of the sphere, assume $\partial U $ to be flat near $x^0 $ and $x_n=0$ I am looking for a concrete example to appreciate whats happening when i define function the following way . Example can be in 1d or 2d . Thanks for ur help.

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$U$ is a open, bounded subset of $\mathbb R^n$. I think flat here means that the $\partial U$ divides the ball symmetrically . I am not pretty sure.

The text clip is from Partial Differential Equations by Lawrence C. Evans, p. 225, Chapter 5. In the second edition (p. 269, Section 5.4), $C^\infty$ has been replaced by $C^1$.

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    What is $U$? What does 'flat' mean?2012-07-16
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    @copper.hat : Sir , even i am not sure what flat means, but i have edited it as i have understood.2012-07-16
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    I don't know what you are trying to do. Perhaps if you gave a reference to the text you clipped?2012-07-16
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    @copper.hat : Sir , its from Evans PDE book . i have posted the reference .2012-07-16
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    I added a Google Books link to the second edition and a note about a change made in that edition.2012-07-16
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    @joriki : Thank you sir .2012-07-16

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