fundamental theorem of calculus for line integrals:en.wikipedia.org/wiki/G \int_C \vec\nabla f(\vec{r}) \cdot d\vec{r} = f(\vec{r_2}) - f(\vec{r_1}) One important property from this theorem is that the result is independent of the path (curve C in the notation) of the ...
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(1.1) with boundary data\Phi =(\varphi ^1,\ldots ,\varphi ^m). Since the free boundary lies on the lower dimensional subspace\{x_{n+1}=0\}, such a problem is usually called athinfree boundary problem. With a slight abuse of notation, whenever it does not create confusion, we wil...
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