Gradient flow for the Boltzmann entropy and Cheeger's energy on time-dependent metric measure spaces

DOI10.1007/s00526-017-1287-5zbMath1398.35098arXiv1611.09522OpenAlexW3103783254MaRDI QIDQ1703147

Eva Kopfer

Publication date: 1 March 2018

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.09522

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonsmooth analysis (49J52) Heat equation (35K05) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Heat kernel (35K08)

Related Items (2)

Metric measure spaces and synthetic Ricci bounds: fundamental concepts and recent developments ⋮ Super-Ricci flows for metric measure spaces

Cites Work

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• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• Gradient flows of time-dependent functionals in metric spaces and applications to PDEs
• The heat equation on manifolds as a gradient flow in the Wasserstein space
• Differentiability of Lipschitz functions on metric measure spaces
• The Dirichlet heat kernel in inner uniform domains: local results, compact domains and non-symmetric forms
• Quantitative stratification and the regularity of mean curvature flow
• Ricci curvature for metric-measure spaces via optimal transport
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• On the geometry of metric measure spaces. I
• Transport inequalities, gradient estimates, entropy and Ricci curvature
• Heat flow on Finsler manifolds
• Gradient flows of non convex functionals in Hilbert spaces and applications
• Ricci flow, entropy and optimal transportation
• The Variational Formulation of the Fokker--Planck Equation
• Heat Flow on Time‐Dependent Metric Measure Spaces and Super‐Ricci Flows
• An Introduction to Partial Differential Equations
• Heat Flow on Alexandrov Spaces
• Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces
• Optimal Transport
• On the heat flow on metric measure spaces: existence, uniqueness and stability

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