On a Circular Membrane Elastically Supported in a Part of Its Boundary (Open)

Summary: Given a circular membrane $\Omega$ which is fixed at 0 on certain parts $\Gamma_0$ of $\partial \Omega$ and elastically supported on the remaining parts $\Gamma_1$, with constant measure C, the problem asks for the position that $\Gamma_1$ must occupy on $\partial \Omega$ in order to maximize the height reached at the center of the membrane.

Classification: Primary, differential equations; Secondary, PDE, classical analysis

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