Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator

P. Delanoë

Annales de l'I.H.P. Analyse non linéaire (1991)

  • Volume: 8, Issue: 5, page 443-457
  • ISSN: 0294-1449

How to cite

top

Delanoë, P.. "Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator." Annales de l'I.H.P. Analyse non linéaire 8.5 (1991): 443-457. <http://eudml.org/doc/78260>.

@article{Delanoë1991,
author = {Delanoë, P.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Monge-Ampère equation; maps between convex domains},
language = {eng},
number = {5},
pages = {443-457},
publisher = {Gauthier-Villars},
title = {Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator},
url = {http://eudml.org/doc/78260},
volume = {8},
year = {1991},
}

TY - JOUR
AU - Delanoë, P.
TI - Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1991
PB - Gauthier-Villars
VL - 8
IS - 5
SP - 443
EP - 457
LA - eng
KW - Monge-Ampère equation; maps between convex domains
UR - http://eudml.org/doc/78260
ER -

References

top
  1. [1] A. Agmon, D. Douglis and L. Nirenberg, Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions, I.Comm. Pure Appl. Math., Vol. 12, 1959, pp. 623-727; II, Ibid., Vol. 17, 1964, pp. 35- 92. Zbl0093.10401MR125307
  2. [2] T. Aubin, Réduction du cas positif de l'équation de Monge-Ampère sur les variétés Kählériennes compactes à la démonstration d'une inégalité, J. Funct. Anal., Vol. 53, 1983, pp. 231-245. 
  3. [3] I. Bakel'man, Generalized Solutions of Monge-Ampère Equations, Dokl. Akad. Nauk. S.S.S.R., Vol. 114:6, 1957, pp. 1143-1145 (in russian). Zbl0114.29602MR95481
  4. [4] L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet Problem for Nonlinear Second-Order Elliptic Equations I. Monge-Ampère equation, Comm. Pure Appl.Math., Vol. 37, 1984, pp. 369-402. Zbl0598.35047MR739925
  5. [5] B. Dacorogna and J. Moser, On a Partial Differential Equation Involving the Jacobian Determinant, Ann. Inst. Henri Poincaré Analyse non linéaire, Vol. 7:1, 1990, pp. 1-26. Zbl0707.35041MR1046081
  6. [6] P. Delanoë, Equations du type de Monge-Ampère sur les variétés Riemanniennes compactes II, J. Funct. Anal., Vol. 41, 1981, pp. 341-353. Zbl0474.58023MR619957
  7. [7] P. Delanoë, Equations de Monge-Ampère en dimension deux, C. R. Acad. Sci. Paris, 294, série I, 1982, pp. 693-696. Zbl0497.35039MR666620
  8. [8] P. Delanoë, Plongements radiaux Sn → Rn+1 à courbure de Gauss positive prescrite, Ann. Sci. Ec. Norm. Sup., Vol. 18, 1985, pp. 635-649. Zbl0594.53039MR839688
  9. [9] P. Delanoë, Remarques sur les variétés localement Hessiennes, Osaka J. Math., Vol. 26, 1989, pp. 65-69. Zbl0754.53021MR991282
  10. [10] P. Delanoë, Viscosity Solutions of Eikonal and Lie Equations on Compact Manifolds, Ann. Global Anal. Geom., Vol. 7:2, 1989, pp. 79-83. Zbl0644.58020MR1032326
  11. [11] E. Hopf, Elementare Bemerkungen über die Lösungen partieller Differential-gleichungen zweiter Ordnung vom elliptischen Typus, Sitz. Ber. Preuß. Akad. Wissensch.Berlin, Math.-Phys. Kl, Vol. 19, 1927, pp. 147-152. Zbl53.0454.02JFM53.0454.02
  12. [12] E. Hopf, A Remark on Linear Elliptic Differential Equations of Second Order, Proc. Am. Math. Soc., Vol. 3, 1952, pp. 791-793. Zbl0048.07802MR50126
  13. [13] N.M. Ivotchkina, The a priori Estimate ∥u ∥2C(Ω) on Convex Solutions of the Dirichlet problem for the Monge-Ampère Equation, Zapisk. Nautchn. Semin. LOMI, Vol. 96, 1980, pp. 69-79. Zbl0472.35040
  14. [14] L.Y. Liao and F. Schulz, Regularity of Solutions of Two-Dimensional Monge-Ampère Equations, Transact. Am. Math. Soc., Vol. 307:1, 1988, pp. 271-277. Zbl0664.35023MR936816
  15. [15] G.M. Lieberman and N.S. Trudinger, Nonlinear Oblique Boundary Value Problems for Nonlinear Elliptic Equations, Transact. Am. Math. Soc., 295:2, 1986, pp. 509-546. Zbl0619.35047MR833695
  16. [16] P.-L. Lions, N.S. Trudinger and J.I.E. Urbas, The Neumann problem for Equations of Monge-Ampère Type, Comm. Pure Appl. Math., Vol. 39, 1986, pp. 539-563. Zbl0604.35027MR840340
  17. [17] L. Nirenberg, On Nonlinear Elliptic Partial Differential Equations and Hölder Continuity, Comm. Pure Appl. Math., Vol. 6, 1953, pp. 103-156. Zbl0050.09801MR64986
  18. [18] A.V. Pogorelov, Monge-Ampère Equations of Elliptic Type, Noordhoff Ltd, 1964. Zbl0133.04902MR180763
  19. [19] F. Schulz, Boundary Estimates for Solutions of Monge-Ampère Equations in the Plane, Ann. Sc. Norm. Sup. Pisa, Vol. 11:3, 1984, pp. 431-440. Zbl0573.35031MR785620
  20. [20] K.-S. Tso, Personal Letters from the Chinese University of Hong-Kong sent on July 12, 1988 and on June 7, 1989. 
  21. [21] J.I.E. Urbas, The Oblique Derivative Problem for Equations of Monge-Ampère Type in Two Dimensions, Preprint, Courant Institute and CMA at Canberra, 1987. Zbl0649.35038MR924435

NotesEmbed ?

top

You must be logged in to post comments.