A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications

Authors:

P. Cannarsa P. Cardaliaguet G. Crasta E. Giorgieri

Affiliation:

(1) Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy;(2) UFR des Sciences et Techniques, Université de Bretagne Occidentale, 6 Av. Le Gorgeu, BP 809, 29285 Brest, France;(3) Dipartimento di Matematica, Università di Roma La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy;(4) Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy

Abstract:

The system of partial differential equations

$$
left{
begin{array}{l}-{rm div}(vDu)=fquad {rm in};{rm Omega}
|Du|-1=0quad {rm in };{v > 0 }
end{array}
right.
$$

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

$int_{{rm Omega}} [h(|Du|)-f(x) u]{rm d}x,$

with f≥ 0, and h≥ 0 possibly non-convex, is also included. Mathematics Subject Classification: Primary 35C15, 49J10, Secondary 35Q99, 49J30

Keywords:

Granular matter Eikonal equation Singularities Semiconcave functions Viscosity solutions Optimal mass transfer Existence of minimizers Distance function Calculus of variations Nonconvex integrands

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