Generalised solutions of Hessian equations

Bulletin of the Australian Mathematical Society

Volumn 56, Issue 3, 1997, Pages 459-466

  Colesanti, Andrea ^a   Salani, Paolo ^a  

^a Dipartimento di Matematica U Dini   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031521507     PISSN: 00049727     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0004972700031257     Document Type: Article

References (12)

1. R.B. Ash, Measure, integration and functional analysis (Academic Press, New York, 1972).
2. I.J. Bakelman, 'Geometric inequalities and existence theorems for convex generalized solutions of n-dimensional Monge-Ampére equations', in Geometric analysis and nonlinear partial differential equations, (I.J. Bakelman, Editor) (Marcel Dekker, New York, 1993), pp. 237-287.
3. V. Bangert, 'Sets with positive reach', Arch. Math. 38 (1982), 54-57.
4. A. Colesanti, 'A Steiner type formula for convex functions', Mathematika (to appear).
5. L. Caffarelli, L. Nirenberg and J. Spruck, 'The Dirichlet problem for nonlinear second order elliptic equations, III: functions of the eigenvalues of the Hessian', Acta Math. 155 (1985), 261-301.
6. H. Federer, 'Curvature measures', Trans. Amer. Math. Soc. 93 (1959), 418-491.
7. J.H.G. Fu, 'Tubular neighborhoods in Euclidean spaces', Duke Math J. 52 (1985), 1025-1046.
8. J. Rauch and B.A. Taylor, 'The Dirichlet problem for the multidimensional Monge-Ampére equation', Rocky Mountain J. Math. 7 (1977), 345-364.
9. R. Schneider, Convex bodies: the Brunn-Minkowski theory (University Press, Cambridge, 1993).
10. N.S. Trudinger, 'On the Dirichlet problem for Hessian equations', Acta Math. 175 (1995), 151-164.
11. N.S. Trudinger, 'Weak Solutions of Hessian equations', (preprint).
12. J.I.E. Urbas, 'Regularity of generalized solutions of Monge-Ampère equations', Math. Z. 197 (1988), 365-393.