The system of partial differential equations -div (vDu) = f in Q vertical bar Du vertical bar - 1 = 0 in {v > 0} arises in the analysis of mathematical models for sandpile growth and in the context of the Monge-Kantorovich optimal mass transport theory. A representation formula for the solutions of a related boundary value problem is here obtained, extending the previous two-dimensional result of the first two authors to arbitrary space dimension. An application to the minimization of integral functionals of the form integral(Omega) [h(vertical bar Du vertical bar)-f(x)u]dx, with f >= 0, and h >= 0 possibly non-convex, is also included.
Cannarsa, P., Cardaliaguet, P., Crasta, G., Giorgieri, E. (2005). A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 24(4), 431-457 [10.1007/s00526-005-0328-7].
A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications
CANNARSA, PIERMARCO;
2005-01-01
Abstract
The system of partial differential equations -div (vDu) = f in Q vertical bar Du vertical bar - 1 = 0 in {v > 0} arises in the analysis of mathematical models for sandpile growth and in the context of the Monge-Kantorovich optimal mass transport theory. A representation formula for the solutions of a related boundary value problem is here obtained, extending the previous two-dimensional result of the first two authors to arbitrary space dimension. An application to the minimization of integral functionals of the form integral(Omega) [h(vertical bar Du vertical bar)-f(x)u]dx, with f >= 0, and h >= 0 possibly non-convex, is also included.| File | Dimensione | Formato | |
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