Some Inequalities of Hardy Type Related to Witten–Laplace Operator on Smooth Metric Measure Spaces
Yanlin Li, Abimbola Abolarinwa, Ali H. Alkhaldi, Akram Ali
Abstract
A complete Riemannian manifold equipped with some potential function and an invariant conformal measure is referred to as a complete smooth metric measure space. This paper generalizes some integral inequalities of the Hardy type to the setting of a complete non-compact smooth metric measure space without any geometric constraint on the potential function. The adopted approach highlights some criteria for a smooth metric measure space to admit Hardy inequalities related to Witten and Witten p-Laplace operators. The results in this paper complement in several aspect to those obtained recently in the non-compact setting.
Topics & Concepts
MathematicsMeasure (data warehouse)Laplace operatorPure mathematicsMetric (unit)Riemannian manifoldMathematical analysisLaplace transformType (biology)Space (punctuation)Manifold (fluid mechanics)Metric spaceInvariant (physics)Mathematical physicsEcologyEngineeringBiologyPhilosophyMechanical engineeringDatabaseEconomicsOperations managementComputer scienceLinguisticsGeometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsAnalytic and geometric function theory