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

Journal of Differential Equations

Volumn 235, Issue 2, 2007, Pages 484-509

  Crasta, Graziano ^a   Malusa, Annalisa ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Distance function; Hamilton Jacobi equations; Mass transport; Minkowski spaces

Indexed keywords

EID: 33847715793     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2007.01.010     Document Type: Article

References (18)

1. Bardi M., and Capuzzo-Dolcetta I. Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Systems Control Found. Appl. (1997), Birkhäuser, Boston
2. Bouchitté G., and Buttazzo G. Characterization of optimal shapes and masses through Monge-Kantorovich equation. J. Eur. Math. Soc. 3 (2001) 139-168
3. 1 under strict convexity. In: Baiocchi C. (Ed). Boundary Value Problems for Partial Differential Equations and Applications. RMA Res. Notes Appl. Math. vol. 29 (1993), Masson, Paris 43-52
4. Cannarsa P., and Cardaliaguet P. Representation of equilibrium solutions to the table problem for growing sandpiles. J. Eur. Math. Soc. (JEMS) 6 (2004) 435-464
5. Cannarsa P., Cardaliaguet P., Crasta G., and Giorgieri E. A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications. Calc. Var. Partial Differential Equations 24 (2005) 431-457
6. Cannarsa P., and Sinestrari C. Semiconcave Functions, Hamilton-Jacobi Equations and Optimal Control. Progr. Nonlinear Differential Equations Appl. vol. 58 (2004), Birkhäuser, Boston
7. Celada P., Perrotta S., and Treu G. Existence of solutions for a class of non-convex minimum problems. Math. Z. 228 (1998) 177-199
8. Cellina A. Minimizing a functional depending on ∇u and on u. Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 339-352
9. Chapman S.J. A hierarchy of models for type-II superconductors. SIAM Rev. 42 (2000) 555-598
10. G. Crasta, A. Malusa, The distance function from the boundary in a Minkowski space, Trans. Amer. Math. Soc., submitted for publication
11. Evans L.C., and Gangbo W. Differential equations methods for the Monge-Kantorovich mass transfer problem. Mem. Amer. Math. Soc. 137 653 (1999) viii+66 pp
12. Gilbarg D., and Trudinger N.S. Elliptic Partial Differential Equations of Second Order (1977), Springer, Berlin
13. Giusti E. Metodi diretti nel calcolo delle variazioni (1994), Unione Matematica Italiana, Bologna
14. Ladyzhenskaya O., and Ural'tseva N. Linear and Quasilinear Elliptic Equations (1968), Academic Press, New York
15. Li Y.Y., and Nirenberg L. The distance function to the boundary, Finsler geometry and the singular set of viscosity solutions of some Hamilton-Jacobi equations. Comm. Pure Appl. Math. 58 (2005) 85-146
16. Lions P.L. Generalized Solutions of Hamilton-Jacobi Equations (1982), Pitman, Boston
17. Prigozhin L. Variational model of sandpile growth. European J. Appl. Math. 7 (1996) 225-235
18. Schneider R. Convex Bodies: The Brunn-Minkowski Theory (1993), Cambridge Univ. Press, Cambridge