发表机构
National Institute of Science Education and Research; Universität Potsdam; Technion - Israel Institute of Technology（国家科学教育研究所; 波茨坦大学; 以色列理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过格林势构造了与p-Schrödinger算子相关的严格正临界Hardy权族，并证明其最佳常数及在ε=0时的最优性，同时推广到图上。
AI 中文摘要
考虑与非紧黎曼流形中区域$\Omega$上定义的$p$-Schrödinger算子相关的次临界泛函$Q$。利用超解构造，我们为$Q$获得一族严格正的临界Hardy权。该构造基于格林势，并假设其具有严格正且在无穷远处消失的电荷。这一族权依赖于参数$0\leq\varepsilon\leq 1$，其一个有趣的新特征是当$\varepsilon=0$时从正临界性过渡到零临界性。此外，我们证明该族的最佳Hardy常数由$c=[(p-1)/p]^{p-1}$给出，并且当$\varepsilon=0$时相应的Hardy权是最优的。我们还证明了在图上类似的结果。
英文摘要
Consider a subcritical functional $Q$ associated with a $p$-Schrödinger operator defined on a domain $Ω$ in noncompact Riemannian manifold. Employing the supersolution construction, we obtain a family of strictly positive critical Hardy weights for $Q$. The construction is based on the Green potential, with a strictly positive charge, which is assumed to vanish at infinity. An interesting new feature of this family, depending on a parameter $0\leq \varepsilon\leq 1$, is the transition from positive-criticality to null-criticality at $\varepsilon=0$. Moreover, we show that the best Hardy constant for this family is given by $c=[(p-1)/p]^{p-1}$, and that for $\varepsilon=0$ the corresponding Hardy weight is optimal. We furthermore, prove an analogous result on graphs.
Comments28 pages
