7 citations · 43 across the 38 of their papers we have counts for
3 papers · 2 filters
Serrin's overdetermined problem on the sphere
Mouhamed Moustapha Fall, Ignace Aristide Minlend, Tobias Weth
We study Serrin's overdetermined boundary value problem \begin{equation*} -Δ_{S^N}\, u=1 \quad \text{ in },\qquad u=0, \; \partial_ηu=\textrm{const} \quad \text{on }…
Unbounded periodic solutions to Serrin's overdetermined boundary value problem
Mouhamed Moustapha Fall, Ignace Aristide Minlend, Tobias Weth
We study the existence of nontrivial unbounded domains in such that the overdetermined problem $$ -Δu = 1 \quad \text{in }, \qquad u=0, \quad \partial_νu=\tex…
On the rate of change of the best constant in the Sobolev inequality
Tom Carroll, Mouhamed Moustapha Fall, Jesse Ratzkin
We estimate the rate of change of the best constant in the Sobolev inequality of a Euclidean domain which moves outward. Along the way we prove an inequality which reverses the usu…