3 problems

Consider the power-like Hamiltonian $H=A|Du|^\gamma$ with $A<0$ and $\gamma\neq2$. Negative-coefficient Liouville conjecture. The Liouville property should hold as in the quadratic…

Let $u$ be a nonnegative solution of … in $\mathbb{R}^N$, where $\beta$ is the parameter associated with the Pucci operator. Liouville conjecture. Any such solution is constant pro…

Let $\mathbb{G}$ be a finitely generated group, and let $\mu$ and $\nu$ be courteous probability measures on $\mathbb{G}$. Liouville invariance conjecture. The random-walk space…