Boundary regularity for solutions of the equation of prescribed Gauss curvature

J. I. E. Urbas

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

  • Volume: 8, Issue: 5, page 499-522
  • ISSN: 0294-1449

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Urbas, J. I. E.. "Boundary regularity for solutions of the equation of prescribed Gauss curvature." Annales de l'I.H.P. Analyse non linéaire 8.5 (1991): 499-522. <http://eudml.org/doc/78263>.

@article{Urbas1991,
author = {Urbas, J. I. E.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Gauss curvature; convex solutions; Hölder continuity; free boundary problem for an auxiliary function; Legendre transformation; general Monge-Ampère equations},
language = {eng},
number = {5},
pages = {499-522},
publisher = {Gauthier-Villars},
title = {Boundary regularity for solutions of the equation of prescribed Gauss curvature},
url = {http://eudml.org/doc/78263},
volume = {8},
year = {1991},
}

TY - JOUR
AU - Urbas, J. I. E.
TI - Boundary regularity for solutions of the equation of prescribed Gauss curvature
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1991
PB - Gauthier-Villars
VL - 8
IS - 5
SP - 499
EP - 522
LA - eng
KW - Gauss curvature; convex solutions; Hölder continuity; free boundary problem for an auxiliary function; Legendre transformation; general Monge-Ampère equations
UR - http://eudml.org/doc/78263
ER -

References

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  5. [5] S.-Y. Cheng and S.-T. Yau, On the Regularity of the Monge-Ampère Equation det (∂2u/∂xi∂xj)=F(x, u), Comm. Pure Appl. Math., Vol. 30, 1977, pp. 41-68. Zbl0347.35019MR437805
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  7. [7] N.M. Ivochkina, An a priori Estimate of ∥u∥C2 (&lt;Ω) for Convex Solutions of the Dirichlet Problem for the Monge-Ampère Equations, Zap. Naucn. Sem. Leningrad, Otdel. Mat. Inst. Steklov (L.O.M.I.), Vol. 96, 1980, pp. 69-79 (Russian). English translation in J. Soviet Math., Vol. 21, 1983, pp. 689-697. Zbl0472.35040
  8. [8] N.M. Ivochkina, Classical Solvability of the Dirichlet Problem for the Monge-Ampère Equation, Zap. Naučn. Sem. Leningrad, Otdel. Mat. Inst. Steklov (L.O.M.I.), Vol. 131, 1983, pp. 72-79. Zbl0522.35028MR718679
  9. [9] D. Kinderlehrer, L. Nirenberg, Regularity in Free Boundary Problems, Ann. Sc. Norm. Sup. Pisa, Vol. 4, (4), 1977, pp. 373-391. Zbl0352.35023MR440187
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  12. [12] F.H. Lin, Behaviour of Nonparametric Solutions and Free Boundary Regularity, Proceedings of the Centre for MathematicalAnalysis, Australian National University, Vol. 12, 1987, pp. 96-116. Zbl0647.35032MR924431
  13. [13] F.H. Lin, Boundary Behaviour of Solutions of Area-Type Problems, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 497-502. Zbl0649.49020
  14. [14] L. Simon, Boundary Regularity for Solutions of the Nonparametric Least Area Problem, Ann. Math., Vol. 103, 1976, pp. 429-455. Zbl0335.49031MR638358
  15. [15] N.S. Trudinger and J.I.E. Urbas, The Dirichlet Problem for the Equation of Prescribed Gauss Curvature, Bull. Austral. Math. Soc., Vol. 28, 1983, pp. 217-231. Zbl0524.35047MR729009
  16. [16] J.I.E. Urbas, Elliptic Equations of Monge-Ampère Type, Thesis, Australian National University, 1984. 
  17. [17] J.I.E. Urbas, The Equation of Prescribed Gauss Curvature Without Boundary Conditions, J. Differential Geom., Vol. 20, 1984, pp. 311-327. Zbl0566.53013MR788283
  18. [18] J.I.E. Urbas, The Generalized Dirichlet Problem for Equations of Monge-Ampère Type, Ann. Inst. Henri-Poincaré -Analyse Non Linéaire, Vol. 3, 1986, pp. 209-228. Zbl0602.35038MR847307
  19. [19] J.I.E. Urbas, Global Hölder Estimates for Equations of Monge-Ampère Type, Invent. Math., Vol. 91, 1988, pp. 1-29. Zbl0674.35026MR918234
  20. [20] J.I.E. Urbas, Regularity of Generalized Solutions of Monge-Ampère Equations, Math. Z., Vol. 197, 1988, pp. 365-393. Zbl0617.35017MR926846
  21. J.I.E. Urbas, Regularity of Almost Extremal Solutions of Monge-Ampère Equations, Proceedings of the Royal Society ofEdinburgh, Vol. 117 A, 1991, pp. 21-29. Zbl0735.35036MR1096216

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