Boundary estimates for solutions of Monge-Ampère equations in the plane

Friedmar Schulz

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1984)

  • Volume: 11, Issue: 3, page 431-440
  • ISSN: 0391-173X

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Schulz, Friedmar. "Boundary estimates for solutions of Monge-Ampère equations in the plane." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 11.3 (1984): 431-440. <http://eudml.org/doc/83940>.

@article{Schulz1984,
author = {Schulz, Friedmar},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Dirichlet problem; Monge-Ampère equation; Hölder condition; differentiable data},
language = {eng},
number = {3},
pages = {431-440},
publisher = {Scuola normale superiore},
title = {Boundary estimates for solutions of Monge-Ampère equations in the plane},
url = {http://eudml.org/doc/83940},
volume = {11},
year = {1984},
}

TY - JOUR
AU - Schulz, Friedmar
TI - Boundary estimates for solutions of Monge-Ampère equations in the plane
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1984
PB - Scuola normale superiore
VL - 11
IS - 3
SP - 431
EP - 440
LA - eng
KW - Dirichlet problem; Monge-Ampère equation; Hölder condition; differentiable data
UR - http://eudml.org/doc/83940
ER -

References

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  1. [1] S. Agmon - A. Douglis - L. Nirfnbifrg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Comm. Pure Appl. Math., 12 (1959), pp. 623-727. Zbl0093.10401MR125307
  2. [2] T. Aubin, Nonlinear analysis on manifolds. Monge-Ampère equations, Springer, New York - Heidelberg - Berlin (1982). Zbl0512.53044MR681859
  3. [3] L. Caffarelli - L. Nirenberg - J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations, I: Monge-Ampère equation (preprint). Zbl0641.35025MR739925
  4. [4] P. Delanoë, Équations de Monge-Ampère en dimension deux, C. R. Acad. Sci., Paris, Ser. I, 294 (1982), pp. 693-696. Zbl0497.35039MR666620
  5. [5] P. Delanoë, Sur certaines équations de Monge-Ampère en dimension n, C. R. Acad. Sci., Paris, Ser. I, 296 (1983), pp. 253-256. Zbl0544.35023MR693786
  6. [6] N.V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations in domains, Izvestija Akad. Nauk SSSR, Ser. Mat., 47 (1983), pp. 75-108. Zbl0578.35024MR688919
  7. [7] L. Nirenberg, On nonlinear elliptic partial differential equations and Hölder continuity, Comm. Pure Appl. Math., 6 (1953), pp. 103-156. Zbl0050.09801MR64986
  8. [8] A.V. Pogorelov, Monge-Ampère equations of elliptic type, Noordhoff, Groningen (1964). Zbl0133.04902MR180763
  9. [9] F. Schulz, Über elliptische Monge-Ampèresche Differentialgleichungen mit einer Bemerkung zum Weylschen Einbettungsproblem, Nachr. Akad. Wiss. Göttingen, II. Math.-Phys. Kl. (1981), pp. 93-108. Zbl0487.35009
  10. [10] F. Schulz, Über die Differentialgleichung rt - S2 = f und das Weylsche Einbettungsproblem, Math. Z., 179 (1982), pp. 1-10. Zbl0535.35021MR643043
  11. [11] F. Schulz, A priori estimates for solutions of Monge-Ampère equations, Arch. Rational Mech. Analysis (to appear). Zbl0572.35039MR786542

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