3 problems

Bonheure-d'Avenia-Pomponio's weak-solution conjecture. The maximizer of ${\mathcal J}_N$ is a weak solution of the related Euler–Lagrange equation. The cited work establishes exist…

The critical wave fronts are described by profiles depending on a reaction term $f$, with the relevant alternatives being either smooth continuation of the limiting profile after s…

Let $\rho\in\mathcal{X}^*\cap L_{loc}^p(\mathbb R^n)$ for some $p>n$, and let $u$ be the minimizer associated with $\rho$. Born–Infeld regularity conjecture. The minimizer satisfie…