A Poincaré type inequality for Hessian integrals

Calculus of Variations and Partial Differential Equations

Volumn 6, Issue 4, 1998, Pages 315-328

  Trudinger, Neu S ^a   Wang, Xu Jia ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009438569     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260050093     Document Type: Article

References (18)

1. Bakelman, I.J.: Variational problems and elliptic Monge-Ampère equations, J. Diff. Geo. 18, 669-999(1983).
2. Caffarelli, L., Nirenberg, L., Spruck, J.: Dirichlet problem for nonlinear second order elliptic equations III, Functions of the eigenvalues of the Hessian, Acta Math. 155, 261-301(1985).
3. Chou, K.S. (Tso, K.): On symmetrization and Hessian equations, J. d'Analyse Math. 52, 94-106(1989).
4. Chou, K.S. (Tso, K.): On a real Monge-Ampère functional, Invent. Math. 101, 425-448(1990).
5. Chou, K.S., Wang, X.J.: Variational solutions to Hessian equations, Australian National University, Mathematics Research Report (ANU MRR) 045-96.
6. Gilbarg, G., Trudinger, N.S.: Elliptic partial differential equations of second order, Second edition, Springer-Verlag, 1983.
7. Ivochkina, N.M.: Solutions of the Dirichlet problem for some equations of Monge-Ampère type, Mat. Sb. 128(1985), 403-415; English translation in Math. USSR Sb. 56, 403-415(1987).
8. Ivochkina, N.M.: Solutions of the Dirichlet problem for some equations of Monge-Ampère type, Mat. Sb. 128(1985), 403-415; English translation in Math. USSR Sb. 56, 403-415(1987).
9. Ivochkina,N.M., Ladyzhenskaya, O.: Flows generated by symmetric functions of the eigenvalues of the Hessian, Zap. Nauchn. Sem. Petersburg, Otdel. Mat. Inst. Steklev.(POMI) 221, 127-144(1995).
10. Krylov, N.V.: Nonlinear elliptic and parabolic equations of second order, Reidel, 1987.
11. Krylov, N.V.: Lectures on fully nonlinear elliptic equations, Lipschitz Lectures, Univ. of Bonn, 1994.
12. Reilly, R.C.: On the Hessian of a function and the curvatures of its graph, Michigan Math. J. 20, 373-383(1973-74).
13. Trudinger, N.S.: The Dirichlet problem for the prescribed curvature equations, Arch. Rat. Mech. Anal. 111, 153-179(1990).
14. Trudinger, N.S.: Isoperimetric inequalities for quermassintegrals, Ann. Inst. H. Poincaré, Non Linéaire, 11, 411-425(1994).
15. Trudinger, N.S.: On the Dirichlet problem for Hessian equations, Acta Math. 175, 151-164(1995).
16. Trudinger, N.S.: On new isoperimetric inequalities and symmetrization, J. Reine Angew. Math. 488 (1997), to appear
17. Trudinger, N.S., Wang, X.J.: Hessian measures, Top. Methods in Nonlinear Analysis (1997), to appear
18. Wang, X.J.: A class of fully nonlinear elliptic equations and related functionals, Indiana Univ. Math. J. 43, 25-54 (1994)