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The conformal plate buckling equation

Sagun Chanillo·Michael K. -H. Kiessling
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Abstract

We study the conformal plate buckling equation (Laplace--Beltrami)^2 u =1, where the L-B operator is for the metric g = e^{2u}g_0, with $g_0$ the standard Euclidean metric on R^2. This conformal elliptic PDE of fourth order is equivalent to the nonlinear system of elliptic PDEs of second order, Delta u +K_g e^(2u)=0, Delta K_g + e^(2u)=0, with x in R^2, describing a conformally flat surface with a Gauss curvature function K_g that is generated self-consistently through the metric's conformal factor.

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Sagun Chanillo, Michael K. -H. Kiessling. 2001-04-18. The conformal plate buckling equation. https://arxiv.org/abs/math/0104183

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