A nonhomogeneous boundary value problem in mass transfer theory

Abstract

We prove a uniqueness result of solutions for a system of PDEs of Monge-Kantorovich type arising in problems of mass transfer theory. The results are obtained under very mild regularity assumptions both on the reference set $\Omega \subset {\mathbf{R}}^n$, and on the (possibly asymmetric) norm defined in $\Omega$. In the special case when $\Omega$ is endowed with the Euclidean metric, our results provide a complete description of the stationary solutions to the tray table problem in granular matter theory.

arXiv comment22 pages, 2 figures

References in corpus (5)

• Hamilton-Jacobi Equations and Distance Functions on Riemannian Manifolds
• The distance function from the boundary in a Minkowski space
• On a system of partial differential equations of Monge-Kantorovich type
• A variational approach to the macroscopic electrodynamics of anisotropic hard superconductors
• A sharp uniqueness result for a class of variational problems solved by a distance function

Cited by in corpus (4)

• A new symmetry criterion based on the distance function and applications to PDE's
• Existence and uniqueness of solutions for a boundary value problem arising from granular matter theory
• On a Differential Model for Sandpiles Growing in a Silo
• A differential model for growing sandpiles on networks