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Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

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Curvature of the boundary vs. normal derivative of the first eigenfunction

You use a local system of coordinates with $x$-axis tangent to the boundary and $y$ along the normal vector; let $y=y(x)$ the equation of the curve, so $u(x,y(x))=0$ ($u=\phi_1$). Differentiating this …
Michael Albanese's user avatar