5 problems

Let $\mathbb{G}=(\mathbb{R}^n,\circ)$ be a stratified Lie group of homogeneous dimension $Q$, let $\Omega\subset\mathbb{G}$ be a bounded open set with smooth boundary, let…

Global existence conjecture. The problem $$ admits a global solution whenever

Critical-exponent conjecture. The numbers $1+\frac{2}{\alpha}$ and $\frac{Q-\alpha}{Q-2-\alpha}$ are the critical exponents for local and global existence of a weak solution of $$,…

Let $\mathrm{G}$ be an $n$-dimensional stratified Lie group with homogeneous dilation weights $(\ell_1,\ell_2,\ldots,\ell_n)$, rescaled so that $\min(\ell_j)=1$, and let…

Let $\mathfrak L$ be a stratified Lie group equipped with its canonical Carnot–Carathéodory distance function, and let $\Upomega$ be a domain. Assume that $\mathfrak L$ is neither…