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 $\Omega\subset\R^n$), whose construction is based on an asymmetric Minkowski distance from the boundary of $\Omega$, was already established in [Crasta - Malusa, The distance function from the boundary in a Minkowski space, 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.
On a system of partial differential equations of Monge-Kantorovich type / Crasta, Graziano; Malusa, Annalisa. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 235:(2007), pp. 484-509. [10.1016/j.jde.2007.01.010]
On a system of partial differential equations of Monge-Kantorovich type
CRASTA, Graziano;MALUSA, ANNALISA
2007
Abstract
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 $\Omega\subset\R^n$), whose construction is based on an asymmetric Minkowski distance from the boundary of $\Omega$, was already established in [Crasta - Malusa, The distance function from the boundary in a Minkowski space, 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.