10 citations · 45 across the 23 of their papers we have counts for
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math.AP2014
Monotonicity of the first Dirichlet eigenvalue of the Laplacian on manifolds of nonpositive curvature
Tom Carroll, Jesse Ratzkin
Let be a complete manifold of nonpositive scalar curvature, let be a suitable domain, and let be the first Dirichlet eigenvalue of the Laplace-Beltrami…
math.AP2014
A reverse Holder inequality for extremal Sobolev functions
Tom Carroll, Jesse Ratzkin
Let , let be a bounded domain with smooth boundary, and let . We prove a reverse-Holder inequality for functions realizing th…
math.NA2014★ 2 cited
A numerical investigation of level sets of extremal Sobolev functions
Stefan Juhnke, Jesse Ratzkin
In this paper we investigate the level sets of extremal Sobolev functions for subcritical exponents p. We conjecture that as p increases the corresponding extremal functions become…