Carlo Mercuri

Unique continuation, nonexistence and bubbling for the critical $p$-Laplace equation in the plane

For $1<p<2$ we prove weak and strong unique continuation properties for the solutions to $\Delta_pu+f(u)=0$ in a planar domain, with $f$ continuous and such that $|f(s)|\leq C|s|^{p-1}$: a solution vanishing on an open set vanishes identically, and so does a solution vanishing to infinite order at a single point. We ca...