Coarse and Precise $L^p$-Green Potential Estimates on Noncompact Riemannian Manifolds - Mathematics > Analysis of PDEsReportar como inadecuado




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Abstract: We are concerned about the coarse and precise aspects of a priori estimatesfor Green-s function of a regular domain for the Laplacian-Betrami operator onany $3\le n$-dimensional complete non-compact boundary-free Riemannian manifoldthrough the square Sobolev-Nash-logarithmic-Sobolev inequalities plus the roughand sharp Euclidean isoperimetric inequalities. Consequently, we are led toevaluate the critical limit of an induced monotone Green-s functional using theasymptotic behavior of the Lorentz norm deficit of Green-s function at theinfinity, as well as the harmonic radius of a regular domain in the Riemannianmanifold with nonnegative Ricci curvature.



Autor: Jie Xiao

Fuente: https://arxiv.org/







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