3 problems

de Figueiredo–do Ó–Ruf conjecture. The supremum $S_{\Omega}\left(\lambda,\frac{N}{N-1}\right)$ should not be attained when $\lambda\geq\alpha_N$. They established attainment for ev…

Blow-up analysis conjecture. A blow-up analysis can be performed in the quasilinear context to prove the existence of extremal functions for $\Phi$ in ${\mathcal B}_1$. This concer…

Let $\Omega\subset\mathbb{R}^{2}$ be a bounded convex domain with smooth boundary, and let $u\in C^{\infty}_{0}(\Omega)$. The Hardy term is defined using the distance to the bounda…