A first-order condition for the independence on p of weak gradients

2022/08/27 by Nicola Gigli, Francesco Nobili · 3 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · doi:10.1016/j.jfa.2022.109686

Abstract

It is well known that on arbitrary metric measure spaces, the notion of minimal p-weak upper gradient may depend on p. In this paper we investigate how a first-order condition of the metric-measure structure, that we call Bounded Interpolation Property, guarantees that in fact such dependence is not present. We also show that the Bounded Interpolation Property is stable for pointed measure Gromov Hausdorff convergence and holds on a large class of spaces satisfying curvature dimension conditions.

Citations

• Independence on p of weak upper gradients on RCD spaces

Cited by

• Mosco-convergence of Cheeger energies on varying spaces satisfying curvature dimension conditions
• Regularity for quasilinear elliptic equations in metric measure spaces
• Stability of local Riemannian Ricci curvature lower bounds

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