Question

Prove that $\lim_{\epsilon \rightarrow 0}\int_{\partial B_\epsilon} (φ∇g · n − g∇φ · n) ds = 2πφ(0, 0)$

score 95 · Answer 1 · 2016-07-03 17:38:51

95

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Prove that $\lim_{\epsilon \rightarrow 0}\int_{\partial B_\epsilon} (φ∇g · n − g∇φ · n) ds = 2πφ(0, 0)$

Published on 03 Jul 2016 - 17:38

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score 131 · Answer 15 · 2017-05-18 19:01:46

131

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List Question

Prove that $\lim_{\epsilon \rightarrow 0}\int_{\partial B_\epsilon} (φ∇g · n − g∇φ · n) ds = 2πφ(0, 0)$

Rellich Integral Identity for Normal Derivatives

Green's theorem for a surface

How to use Green's theorem?

How to calculate the area of an asteroid using Green's theorem

Work done in a Vector Field / Green's Theorem with Parametrization

Green's Theorem with logarithm

Prove for any closed curve $C$ then the path integral is independent of the path between points $p$ and $q$

Green's theorem on a trigonometric curve

Green's Theorem for area using polar coordinates

Apply Green's theorem for $\iint_D (x+2y)dxdy$ on region bounded with $x = t- \sin (t), y = 1 - \cos (t)$.

Greens theorem over a trapezoid

Applying Green's Theorem to evaluate line integral

Applications of Green's Theorem for which there are no obvious simpler proofs

Are single points or rectangles of area $0$ simple closed curves?

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