黎曼流形上p-Laplace算子的Liouville定理
A Liouville Theorem of the p-Laplace Operator on Riemannian Manifolds

主要研究非紧黎曼流形上微分不等式Δ_pu+u^σ≤0的Liouville定理，其中1＜p ≤ 2，σ > p-1，证明了当积分条件$\mathop {\lim {\rm{inf}}}\limits_{t \searrow 0} {t^{\frac{\sigma }{{\sigma - p + 1}}}}\int_1^\infty {\frac{{\mu \left( {{B_r}} \right)}}{{{r^{\frac{{\sigma \left( {p + 1} \right) - \left( {p - 1} \right)}}{{\sigma - p + 1}} + t}}}}} {\rm{d}}r ＜ \infty $成立时上面不等式不存在弱意义下的非平凡的非负解.
In this paper we study the Liouville theorem of the differential inequality Δ_pu+u^σ ≤ 0 on complete noncompact Riemannian manifolds, where 1 < p ≤ 2, σ > p-1. We prove that the above inequality does not exist nontrivial nonnegative solutions in the weak sense if the integral condition $\mathop {\lim {\rm{inf}}}\limits_{t \searrow 0} {t^{\frac{\sigma }{{\sigma - p + 1}}}}\int_1^\infty {\frac{{\mu \left( {{B_r}} \right)}}{{{r^{\frac{{\sigma \left( {p + 1} \right) - \left( {p - 1} \right)}}{{\sigma - p + 1}} + t}}}}} {\rm{d}}r < \infty $ satisfies