128 citations · 387 across the 40 of their papers we have counts for
46 papers
On 2D Harmonic Extensions of Vector Fields and Stellarator Coils
Adam J. Golab, James C. Robinson, José L. Rodrigo
We consider a problem relating to magnetic confinement devices known as stellarators. Plasma is confined by magnetic fields generated by current-carrying coils, and here we investi…
Explicit characterisation of the fractional power spaces of the Dirichlet Laplacian and Stokes operators
Karol W. Hajduk, James C. Robinson
We identify explicitly the fractional power spaces for the Dirichlet Laplacian and Dirichlet Stokes operators using the theory of real interpolation. The results are not new,…
Using periodic boundary conditions to approximate the Navier-Stokes equations on and the transfer of regularity
James C. Robinson
This paper considers solutions of the three-dimensional Navier--Stokes equations on the periodic domains as the domain size , and compares them to…
On the Assouad dimension of differences of self-similar fractals
Alexandros Margaris, Eric J. Olson, James C. Robinson
If is a set with finite Assouad dimension, it is known that the Assouad dimension of does not necessarily obey any non-trivial bound in terms of the Assouad dimension of…
Some comments on Laakso graphs and sets of differences
Alexandros Margaris, James C. Robinson
We recall a variation of a construction due to Laakso \cite{LA}, also used by Lang and Plaut \cite{LA} of a doubling metric space that cannot be embedded into any Hilbert space…
Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces
Charles L. Fefferman, Karol W. Hajduk, James C. Robinson
We approximate functions defined on smooth bounded domains by elements of the eigenspaces of the Laplacian or the Stokes operator in such a way that the approximations are bounded…