2 problems

Let $M$ be a Riemannian manifold, let $E$ be a Hermitian vector bundle over $M$, and let $V$ be a potential satisfying Assumption A: $V=V_{+}+V_{-}$, with $V_{+}(x)8e0$ and…

Let $p\in(2,\infty)$, let $B_1$ be the unit ball, and let $\Delta_p u\coloneqq\operatorname{div}(|Du|^{p-2}Du)$. A function is locally of class $C^{1,\alpha}$ if it has locally Höl…