Uniqueness of \(L^ 1\) solutions for the Laplace equation and the heat equation on Riemannian manifolds
From MaRDI portal
Publication:2266458
DOI10.4310/jdg/1214439287zbMath0561.53045OpenAlexW1543858547WikidataQ115187494 ScholiaQ115187494MaRDI QIDQ2266458
Publication date: 1984
Published in: Journal of Differential Geometry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4310/jdg/1214439287
Global Riemannian geometry, including pinching (53C20) Heat and other parabolic equation methods for PDEs on manifolds (58J35)
Related Items (34)
A remark on the maximum principle and stochastic completeness ⋮ Heat kernel on smooth metric measure spaces and applications ⋮ A new topological approach to the \(L^{\infty }\)-uniqueness of operators and the \(L^{1}\)-uniqueness of Fokker--Planck equations ⋮ Li-Yau inequalities in geometric analysis ⋮ The submartingale property and Liouville type theorems ⋮ Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds ⋮ Hamilton's gradient estimates and a monotonicity formula for heat flows on metric measure spaces ⋮ Heat kernel estimate for the Laplace-Beltrami operator under Bakry-Émery Ricci curvature condition and applications ⋮ Uniqueness in weighted Lebesgue spaces for an elliptic equation with drift on manifolds ⋮ New Laplacian comparison theorem and its applications to diffusion processes on Riemannian manifolds ⋮ Some \(L^p\) Liouville theorems on Finsler measure spaces ⋮ Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations. II ⋮ Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds ⋮ On the uniqueness for the heat equation on complete Riemannian manifolds ⋮ \(L^q\) harmonic functions on graphs ⋮ \(L^p\)-Liouville theorems on complete smooth metric measure spaces ⋮ Uniqueness for the heat equation in Riemannian manifolds ⋮ Some Liouville-type theorems for harmonic functions on Finsler manifolds ⋮ LIOUVILLE PROPERTY FOR <i>f</i>-HARMONIC FUNCTIONS WITH POLYNOMIAL GROWTH ⋮ Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries ⋮ \(L^1\)-uniqueness of the Fokker-Planck equation on a Riemannian manifold ⋮ Rigidity of vector valued harmonic maps of linear growth ⋮ Stochastic completeness for graphs with curvature dimension conditions ⋮ Boundary behavior of harmonic functions on manifolds ⋮ Implications of energy conditions on standard static space-times ⋮ Default functions and Liouville type theorems based on symmetric diffusions ⋮ Heat kernel on smooth metric measure spaces with nonnegative curvature ⋮ The heat equation and harmonic maps of complete manifolds ⋮ Stochastic completeness and gradient representations for Sub-Riemannian manifolds ⋮ The heat flow and harmonic maps between complete manifolds ⋮ Intertwining relations for diffusions in manifolds and applications to functional inequalities ⋮ Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds ⋮ Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds ⋮ On the \(L^\infty \)-uniqueness of symmetric diffusion operators on complete non-compact Riemannian manifolds
This page was built for publication: Uniqueness of \(L^ 1\) solutions for the Laplace equation and the heat equation on Riemannian manifolds