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- W2952957917 abstract "The torsion function of a convex planar domain has convex level sets, but explicit formulae are known only for rectangles and ellipses. Here we study the torsion function on convex planar domains of high eccentricity. We obtain an approximation for the torsion function 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 compare the behaviour of the torsion function and the first eigenfunction of the Dirichlet Laplacian around their respective maxima." @default.
- W2952957917 created "2019-06-27" @default.
- W2952957917 creator A5083001314 @default.
- W2952957917 date "2018-09-24" @default.
- W2952957917 modified "2023-09-27" @default.
- W2952957917 title "The torsion function of convex domains of high eccentricity" @default.
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- W2952957917 hasPublicationYear "2018" @default.
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