Sophie Sun

Parameter-uniform Robin uniqueness on large dilations

Berestycki and Graham proved large-dilation uniqueness for bounded positive solutions of \[ -\Delta u=f(u)\quad\hbox{in }\kappa\Omega, \qquad u+\alpha\partial_\nu u=0\quad\hbox{on }\partial(\kappa\Omega),\] when $\alpha$ is fixed, and remarked that the dilation threshold should not depend on $\alpha$. We show that it d...