Fetching the paper…

Reading the bibliography…

2018

The torsion function of convex domains of high eccentricity

Beck, Thomas

Original
PDF
Post on X

Understand

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.

The torsion function of convex domains of high eccentricity · Around

Built on

L. G. Makar-Limanov
1971
Earlier work this paper cites.
H. J. Brascamp
1976
Earlier work this paper cites.
D. Gilbarg
1983
Earlier work this paper cites.
L. E. Payne
1983
Earlier work this paper cites.
D. Jerison
1995
Earlier work this paper cites.

Similar

D. Grieser
1996
Cited alongside, same era.
D. Grieser
1998
Cited alongside, same era.
M. Filoche
2012
Cited alongside, same era.
D. Arnold, G. David, D. Jerison, S. Mayboroda
2016
Cited alongside, same era.

Then

B. Benson
2016
Later among the works it cites.
S. Steinerberger
2017
Later among the works it cites.
M. Rachh
2018
Closest in time.
S. Steinerberger
2018
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…