2 problems

Concentration conjecture. As $\gamma$ varies in the stated regime, $u_\gamma$ converges simply to the characteristic function of the point $\{0\}$.

Higher-dimensional convergence conjecture. The sequence $cv_n$ is bounded in $W_0^{1,2}(\Omega)\cap L^\infty(\Omega)$ and therefore converges, up to subsequences, to a bounded nonn…