On the maximum principle for principal curvatures

• Autorzy: Nina M. Ivochkina
• Języki publikacji: EN

Abstrakty

EN

The paper contains the estimates from above of the principal curvatures of the solution to some curvature equations. A correction of the author's previous argument is presented.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 115-126

Daty

wydano

1996

Twórcy

autor

Nina M. Ivochkina

• St.-Petersburg State University of Architecture and Civil Engineering, 2-Krasnoarmeiskaya, 4, 198005 St.-Petersburg, Russia

Bibliografia

• [1] 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.
• [2] L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second-order elliptic equations IV. Starshaped compact Weingarten hypersurfaces, in: Current Topics in Partial Differential Equations, Y. Olya, K. Kasahara and N. Shimajura (eds.), Kinokunize Co., Tokyo, 1986, 1-26.
• [3] L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second order elliptic equations V. The Dirichlet problem for Weingarten hypersurfaces, Comm. Pure Appl. Math. 41 (1988), 47-70.
• [4] N. M. Ivochkina, A description of the stability cones generated by differential operators of Monge-Ampère type, Mat. Sb. 122 (1983), 265-275 (in Russian); English transl. in Math. USSR-Sb. 50 (1985).
• [5] N. M. Ivochkina, Solution of the Dirichlet problem for some equations of Monge-Ampère type, Mat. Sb. 128 (1985), 403-415 (in Russian); English transl. in Math. USSR-Sb. 56 (1987).
• [6] N. M. Ivochkina, Solution of the Dirichlet problem for the m-th order curvature equations, Mat. Sb. 180 (1989), 867-887 (in Russian); English transl. in Math. USSR-Sb. 67 (1990).
• [7] N. M. Ivochkina, The Dirichlet problem for m-th order curvature equations, Algebra i Analiz 2 (3) (1990), 192-217 (in Russian); English transl. in Leningrad Math. J. 2 (1991).
• [8] P. L. Lions, Sur les équations de Monge-Ampère I, Manuscripta Math. 41 (1983), 1-43.
• [9] N. S. Trudinger, The Dirichlet problem for the prescribed curvature equations, Arch. Rational Mech. Anal. 111 (1990), 153-179.
• [10] N. S. Trudinger, Isoperimetric inequalities for quermassintegrals, preprint CMA-MR11-93.