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.
A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications / P., Cannarsa; P., Cardaliaguet; Crasta, Graziano; E., Giorgieri. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 24:4(2005), pp. 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
CRASTA, Graziano;
2005
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
