Hölder regularity of the normal distance with an application to a PDE model for growing sandpiles

DOI10.1090/S0002-9947-07-04259-6zbMath1115.58015MaRDI QIDQ3425955

Piermarco Cannarsa, Elena Giorgieri, Pierre Cardaliaguet

Publication date: 7 March 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

singularitiesviscosity solutionsHölder continuous functionssemiconcave functionsEikonal equationnormal distance

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Special properties of functions of several variables, Hölder conditions, etc. (26B35) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (5)

Granular matter and the time-dependent viscous eikonal equation ⋮ A new symmetry criterion based on the distance function and applications to PDE's ⋮ On the characterization of some classes of proximally smooth sets ⋮ Equivalent formulations for Monge-Kantorovich equation ⋮ A hyperbolic model for granular flow

Cites Work

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• Propagation of singularities for solutions of nonlinear first order partial differential equations
• Representation of equilibrium solutions to the table problem for growing sandpiles
• Mathematical theory of medial axis transform
• Hamilton-Jacobi equations and distance functions on Riemannian manifolds
• A boundary value problem for a PDE model in mass transfer theory: representation of solutions and applications
• The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations
• Differential equations methods for the Monge-Kantorovich mass transfer problem
• The Lipschitz continuity of the distance function to the cut locus

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