Representation of equilibrium solutions to the table problem of growing sandpiles

Cannarsa, Piermarco, and Cardaliaguet, Pierre. "Representation of equilibrium solutions to the table problem of growing sandpiles." Journal of the European Mathematical Society 006.4 (2004): 435-464. <http://eudml.org/doc/277314>.

@article{Cannarsa2004,
abstract = {In the dynamical theory of granular matter the so-called table problem consists in studying the evolution of a heap of matter poured continuously onto a bounded domain $\Omega \subset \mathbb \{R\}^2$. The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a system, also connected with other mathematical models such as the Monge–Kantorovich problem, is the object of this paper. Our main result is an integral representation formula for the solution, in terms of the boundary curvature and of the normal distance to the cut locus of $\Omega $.},
author = {Cannarsa, Piermarco, Cardaliaguet, Pierre},
journal = {Journal of the European Mathematical Society},
keywords = {granular matter; eikonal equation; singularities; semiconcave functions; viscosity solutions; optimal mass tranfer; granular matter; eikonal equation; semiconcave function; viscosity solutions; optimal mass transfer},
language = {eng},
number = {4},
pages = {435-464},
publisher = {European Mathematical Society Publishing House},
title = {Representation of equilibrium solutions to the table problem of growing sandpiles},
url = {http://eudml.org/doc/277314},
volume = {006},
year = {2004},
}

TY - JOUR
AU - Cannarsa, Piermarco
AU - Cardaliaguet, Pierre
TI - Representation of equilibrium solutions to the table problem of growing sandpiles
JO - Journal of the European Mathematical Society
PY - 2004
PB - European Mathematical Society Publishing House
VL - 006
IS - 4
SP - 435
EP - 464
AB - In the dynamical theory of granular matter the so-called table problem consists in studying the evolution of a heap of matter poured continuously onto a bounded domain $\Omega \subset \mathbb {R}^2$. The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a system, also connected with other mathematical models such as the Monge–Kantorovich problem, is the object of this paper. Our main result is an integral representation formula for the solution, in terms of the boundary curvature and of the normal distance to the cut locus of $\Omega $.
LA - eng
KW - granular matter; eikonal equation; singularities; semiconcave functions; viscosity solutions; optimal mass tranfer; granular matter; eikonal equation; semiconcave function; viscosity solutions; optimal mass transfer
UR - http://eudml.org/doc/277314
ER -