Yau and Souplet-Zhang type gradient estimates on Riemannian manifolds with boundary under Dirichlet boundary condition
Keita Kunikawa, Yohei Sakurai
Abstract
In this paper, on Riemannian manifolds with boundary, we establish a Yau type gradient estimate and Liouville theorem for harmonic functions under Dirichlet boundary condition. Under a similar setting, we also formulate a Souplet-Zhang type gradient estimate and Liouville theorem for ancient solutions to the heat equation.
Topics & Concepts
MathematicsBoundary (topology)Dirichlet boundary conditionHarmonic functionMathematical analysisType (biology)Dirichlet distributionZhàngBoundary value problemMixed boundary conditionRicci-flat manifoldHarmonicPure mathematicsGeometryPhysicsGeologyLawScalar curvatureCurvaturePolitical scienceQuantum mechanicsChinaPaleontologyNonlinear Partial Differential EquationsGeometric Analysis and Curvature FlowsNumerical methods in inverse problems