On a system of partial differential equations of Monge-Kantorovich type

Details On a system of partial differential equations of Monge-Kantorovich type On a system of partial differential equations of Monge-Kantorovich type

2006-12-09

arxiv.org/abs/math/0612227v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

We consider a system of PDEs of Monge-Kantorovich type arising from models in granular matter theory and in electrodynamics of hard superconductors. The existence of a solution of such system (in a regular open domain $\Omega\subset\mathbb{R}^n$), whose construction is based on an asymmetric Minkowski distance from the boundary of $\Omega$, was already established in [G. Crasta and A. Malusa, The distance function from the boundary in a Minkowski space, to appear in Trans. Amer. Math. Soc.]. In this paper we prove that this solution is essentially unique. A fundamental tool in our analysis is a new regularity result for an elliptic nonlinear equation in divergence form, which is of some interest by itself.

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