发表机构
Sichuan University（四川大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对芬斯勒测度空间上的两类$(p,q)$-拉普拉斯不等式，在势函数满足积分增长条件时证明非负弱解几乎处处为零，核心方法为非线性容量法。
AI 中文摘要
我们在前向测地完备且非紧、具有有限可逆性的芬斯勒测度空间$(M,F,m)$上，研究$(p,q)$-拉普拉斯椭圆微分不等式$$\Delta^{m}_{p}u(x)+\Delta^{m}_{q}u(x)+V(x)u^{s}(x)\leq 0$$及相关抛物微分不等式$$\partial_t u(x,t) \geq \Delta^{m}_{p}u(x,t)+\Delta^{m}_{q}u(x,t)+V(x,t)u^{s}(x,t)$$非负弱解的刘维尔性质。在正势函数在特定环形域上满足若干组积分增长条件时，我们证明任意非负弱解几乎处处为零，结果的证明主要基于非线性容量方法。
英文摘要
We study the Liouville property for nonnegative weak solutions of the $(p,q)$-Laplacian elliptic differential inequality $$Δ^{m}_{p}u(x)+Δ^{m}_{q}u(x)+V(x)u^{s}(x)\leq 0$$ and the associated parabolic differential inequality $$\partial_t u(x,t) \geq Δ^{m}_{p}u(x,t)+Δ^{m}_{q}u(x,t)+V(x,t)u^{s}(x,t)$$ on a forward geodesically complete noncompact Finsler measure space $(M,F,m)$ with finite reversibility. Under several sets of integral growth conditions on the positive potential function over certain annular domains, we prove that any nonnegative weak solution vanishes almost everywhere. The proofs of our results are essentially based on the nonlinear capacity method.
Comments32 pages; all comments are welcome!
