论文标题
足够的标准，可以在Finsler歧管上获得强硬的不平等现象
Sufficient criteria for obtaining Hardy inequalities on Finsler manifolds
论文作者
论文摘要
我们建立了涉及重量功能的耐力不平等，不一定是可逆的鳍式歧管。我们证明，重量函数的超谐调性提供了足够的条件来获得耐寒性不平等。也就是说，如果$ρ$是一种非负功能，而$ - \boldsymbolδρ\ geq 0 $在弱的意义上，其中$ \boldsymbolδ$是$ \boldsymbolΔρ= \boldsymbolδρ= \ m mathrm {div}（\ boldsymbol {\ boldSymbol { D'Ambrosio和Dipierro中的Hardy不平等现象（Ann。St。H。Poincaré，2013年）。 通过扩展获得的结果，我们证明了加权的caccioppoli型不平等，gagliardo-nirenberg不平等和Heisenberg-pauli-weyl的不确定性原理，完全是芬斯勒歧管。此外，我们通过借助距离函数来定义重量函数，在Finsler-Hadamard歧管上呈现一些耐力的不平等。最后，我们将加权的硬性质量扩展到有界几何形状的一类芬斯勒歧管。
We establish Hardy inequalities involving a weight function on complete, not necessarily reversible Finsler manifolds. We prove that the superharmonicity of the weight function provides a sufficient condition to obtain Hardy inequalities. Namely, if $ρ$ is a nonnegative function and $-\boldsymbolΔ ρ\geq 0$ in weak sense, where $\boldsymbolΔ$ is the Finsler-Laplace operator defined by $ \boldsymbolΔ ρ= \mathrm{div}(\boldsymbol{\nabla} ρ)$, then we obtain the generalization of some Riemannian Hardy inequalities given in D'Ambrosio and Dipierro (Ann. Inst. H. Poincaré, 2013). By extending the results obtained, we prove a weighted Caccioppoli-type inequality, a Gagliardo-Nirenberg inequality and a Heisenberg-Pauli-Weyl uncertainty principle on complete Finsler manifolds. Furthermore, we present some Hardy inequalities on Finsler-Hadamard manifolds with finite reversibility constant, by defining the weight function with the help of the distance function. Finally, we extend a weighted Hardy-inequality to a class of Finsler manifolds of bounded geometry.
