Can some one explain please what is exactly of this theorem i dont understand even one word
i don't understand the notations also please ..
thank you
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$u_{x_i}$ is the partial derivative of the function $u$ wrt $x_i$ of the function $u:U\rightarrow \mathbb{R}$ and $\nu^i$ the $i$-th component of the outward pointing unit normal vector to $\partial U$ This seems to be from the appendix of Evan's book on partial differential equations, You can find more comprehensive explanations in many other books – Peter Melech Jan 28 '19 at 13:20
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@PeterMelech..where i get proof for this theorem – Inverse Problem Jan 28 '19 at 13:23
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In my little library at home I just found one here: https://www.springer.com/de/book/9783834823748 unfortunately in German, but wait, I'll try to find a source online, I'm sure there are many – Peter Melech Jan 28 '19 at 13:29
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Here: https://www.ams.org/journals/tran/1945-058-00/S0002-9947-1945-0013786-6/S0002-9947-1945-0013786-6.pdf – Peter Melech Jan 28 '19 at 13:30
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@PeterMelech...how do we define $v^i$ – Inverse Problem Jan 28 '19 at 13:32
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If $U$ is a compact set and $\partial U$ a smooth manifold, for every $x\in\partial U$ there exists exactly one vector of length one, orthogonal to the tangent space $T_x(\partial U)$ that is "pointing outward", You will find all this in any appropriate book that includes a chapter about integration on manifolds – Peter Melech Jan 28 '19 at 13:39