Keywords
- Elliptic Equation
- Dirichlet Problem
- Nonlinear Elliptic Equation
- Order Elliptic Equation
- Convex Solution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A.D. Aleksandrov, Dirichlet's problem for the equation Det‖zij‖=φ(zi,…,znz,x1,…,xn), Vestnik Leningrad Univ. 13 (1958), 5–24, [Russian].
I. Ya. Bakel'man, The Dirichlet problem for equations of Monge-Ampère type and their n-dimensional analogues, Dokl. Akad. Nauk, SSSR 126 (1959), 923–926, [Russian].
I. Ya. Bakel'man, The Dirichlet problem for the elliptic n-dimensional Monge-Ampere equations and related problems in the theory of quasilinear equations, Proceedings of Seminar on Monge-Ampère Equations and Related Topics, Firenze 1980), Instituto Nazionale di Alta Matematica, Roma, (1982), 1–78.
E. Calabi, Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens, Michigan Math. J. 5 (1958), 105–126.
L. Caffarelli, L. Nirenberg, J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations, I. Monge-Ampère equation, Comm. Appl. Math. 37 (1984), 369–402.
L. Caffarelli, J.J. Kohn, L. Nirenberg, J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations II. Complex Monge-Ampère and uniformly elliptic equations, Comm. Pure Appl. Math. 38 (1985), 209–252.
S.-Y. Cheng, S.-T. Yau. On the regularity of the solution of the n-dimensional Minkowski problem, Comm. Pure Appl. Math. 29 (1976), 495–516.
L.C. Evans, Classical solutions of fully nonlinear, convex, second order elliptic equations, Comm. Pure Appl. Math. 35 (1982), 333–363.
D. Gilbarg, N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, Second Edition, 1983.
N.M. Ivochkina, Construction of a priori bounds for convex solutions of the Monge-Ampère equation by integral methods, Ukrain. Mat. Z. 30 (1978), 45–53, [Russian].
N.M. Ivochkina, An apriori estimate of \(\left\| u \right\|_{C^2 (\bar \Omega )}\) for convex solutions of the Dirichlet problem for the Monge-Ampère equations, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 96 (1980), 69–79, [Russian]. English translation in J. Soviet Math. 21 (1983), 689–697.
N.M. Ivochkina, Classical solvability of the Dirichlet problem for the Monge-Ampère equation, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 131 (1983), 72–79.
N.V. Kyrlov, Boundedly inhomogeneous elliptic and parabolic equations, Izv, Akad. Nauk. SSSR 46 (1982), 487–523, [Russian]. English translation in Math. USSR Izv. 20 (1983), 459–492.
N.V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations in a domain, Izv. Akad. Nauk. SSSR 47 (1983), 75–108, [Russian].
N.V. Krylov, On degenerative nonlinear elliptic equations, Mat. Sb. (N.S.) 120 (1983), 311–330, [Russian].
G.M. Lieberman, N.S. Trudinger, Nonlinear oblique boundary value problems for nonlinear elliptic equations. Aust. Nat. Univ. Centre for Math. Anal. Research Report R24 (1984).
P.-L. Lions, Sur les équations de Monge-Ampère I, Manuscripta Math. 41 (1983), 1–44.
P.-L. Lions, Sur les équations de Monge-Ampère II, Arch. Rational Mech. Anal. (to appear).
P.-L. Lions, N.S. Trudinger, Linear oblique derivative problems for the uniformly elliptic Hamilton-Jacobi-Bellman equation, Math. Zeit. (to appear).
P.-L. Lions, N.S. Trudinger, J.I.E. Urbas, The Neumann problem for equations of Monge-Ampère type. Aust. Nat. Univ. Centre for Math. Anal. Research Report R16 (1985).
A.V. Pogorelov, The Dirichlet problem for the n-dimensional analogue of the Monge-Ampère equation, Dokl. Akad. Nauk. SSSR 201 (1971), 790–793, [Russian]. English translation in Soviet Math. Dokl. 12 (1971), 1727–1731.
A.V. Pogorelov, The Minkowski multidimensional problem, J. Wiley, New York, 1978.
F. Schultz, A remark on fully nonlinear, concave elliptic equations, Proc. Centre for Math. Anal. Aust. Nat. Univ. 8, (1984), 202–207.
N.S. Trudinger, Boundary value problems for fully nonlinear elliptic equations. Proc. Centre for Math. Anal. Aust. Nat. Univ. 8 (1984), 65–83.
N.S. Trudinger, Regularity of solutions of fully nonlinear elliptic equations. Boll. Un. Mat. Ital., 3-A (1984), 421–430. II Aust. Nat. Univ. Centre for Math. Anal. Research Report R38 (1984).
N.S. Trudinger, J.I.E. Urbas, The Dirichlet problem for the equation of prescribed Gauss curvature, Bull. Austral. Math. Soc. 28 (1983), 217–231.
N.S. Trudinger, J.I.E. Urbas, On second derivative estimates for equations of Monge-Ampère type, Bull. Austral. Math. Soc. 30 (1984), 321–334.
J.I.E. Urbas, Some recent results on the equation of prescribed Gauss curvature, Proc. Centre for Math. Anal. Aust. Nat. Univ. 8 (1984), 215–220.
J.I.E. Urbas, The equation of prescribed Gauss curvature without boundary conditions, J. Differential Geometry (to appear).
J.I.E. Urbas, The generalized Dirichlet problem for equation of Monge-Ampère type. Ann. L'Inst. Henri Poincaré, (to appear).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Equadiff 6 and Springer-Verlag
About this paper
Cite this paper
Trudinger, N.S. (1986). Classical boundary value problems for Monge-Ampère type equations. In: Vosmanský, J., Zlámal, M. (eds) Equadiff 6. Lecture Notes in Mathematics, vol 1192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076078
Download citation
DOI: https://doi.org/10.1007/BFb0076078
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16469-2
Online ISBN: 978-3-540-39807-3
eBook Packages: Springer Book Archive
