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- W2894535623 abstract "The torsion function of a convex planar domain Ω has convex level sets, but explicit formulae are known only for rectangles and ellipses. Here we study the torsion function when the eccentricity of the domain is large. We obtain an approximation for the torsion function on any convex planar domain by viewing the domain as a perturbation of a rectangle in order to define an approximate Green’s function for the Laplacian. For a class of convex domains we use this approximation to establish sharp bounds on the Hessian and the infinitesimal shape of the level sets around its maximum. We also use these results to construct examples demonstrating contrasting behaviour of the torsion function and the first eigenfunction of the Dirichlet Laplacian around their respective maxima." @default.
- W2894535623 created "2018-10-05" @default.
- W2894535623 creator A5083001314 @default.
- W2894535623 date "2019-05-28" @default.
- W2894535623 modified "2023-09-24" @default.
- W2894535623 title "The Torsion Function of Convex Domains of High Eccentricity" @default.
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- W2894535623 doi "https://doi.org/10.1007/s11118-019-09785-9" @default.
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