A priori interior gradient bounds for solutions to elliptic Weingarten equations

Nicholas J. Korevaar

Annales de l'I.H.P. Analyse non linéaire (1987)

  • Volume: 4, Issue: 5, page 405-421
  • ISSN: 0294-1449

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Korevaar, Nicholas J.. "A priori interior gradient bounds for solutions to elliptic Weingarten equations." Annales de l'I.H.P. Analyse non linéaire 4.5 (1987): 405-421. <http://eudml.org/doc/78138>.

@article{Korevaar1987,
author = {Korevaar, Nicholas J.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {maximum principle; a priori interior gradient bounds; smooth solutions; Weingarten equation; interior barrier surface; prescribed mean curvature equation},
language = {eng},
number = {5},
pages = {405-421},
publisher = {Gauthier-Villars},
title = {A priori interior gradient bounds for solutions to elliptic Weingarten equations},
url = {http://eudml.org/doc/78138},
volume = {4},
year = {1987},
}

TY - JOUR
AU - Korevaar, Nicholas J.
TI - A priori interior gradient bounds for solutions to elliptic Weingarten equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1987
PB - Gauthier-Villars
VL - 4
IS - 5
SP - 405
EP - 421
LA - eng
KW - maximum principle; a priori interior gradient bounds; smooth solutions; Weingarten equation; interior barrier surface; prescribed mean curvature equation
UR - http://eudml.org/doc/78138
ER -

References

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  2. [2] I. Bakelman and I. Kantor, Existence of Spherically Homeomorphic Hypersurfaces in Euclidean Space with Prescribed Mean Curvature, Geometry and Topology, Vol. 1, 1974, pp. 3-10, Leningrad. 
  3. [3] E. Bombieri, E. Di Giorgi and M. Miranda, Una maggiorazione a priori relative alle ipersupertici minimali nonparametriche, Arch. Rat. Mech. Anal, Vol. 32, 1969, pp. 255-269. Zbl0184.32803
  4. [4] L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet Problem for Nonlinear Second Order Elliptic Equations. I. Monge-Ampère Equations, Comm. Pure Appl. Math., Vol. 37, 1984, pp. 369-402. Zbl0598.35047MR739925
  5. [5] L. Caffarelli, J.J. Kohn, L. Nirenberg and J. Spruck, The Dirichlet Problem for Nonlinear Second Order Equations. II. Complex Monge-Ampère, and uniformly Elliptic, Equations, Comm. Pure Appl. Math., Vol. 38, 1985, pp. 209-252. Zbl0598.35048MR780073
  6. [6] L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet Problem for Nonlinear Second Order Elliptic Equations. III. Functions of eigenvalues of the Hessian, Acta. Math. (to appear). Zbl0654.35031MR806416
  7. [7] L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear Second Order Elliptic Equations. IV. Starshaped Compact Weingarten Hypersurfaces (to appear). Zbl0672.35027MR1112140
  8. [8] R. Finn, New Estimates for Equations of Minimal Surface Type, Arch. Rat. Mech. Anal., Vol. 14, 1963, pp. 337-375. Zbl0133.04601MR157096
  9. [9] L. Gårding, An Inequality for Hyperbolic Polynomials, J. Math. and Mechanics, Vol. 8, 1959, pp. 957-965. Zbl0090.01603MR113978
  10. [10] N.M. Ivočkina, The Integral Method of Barrier Functions and the Dirichlet Problem for Equations with Operators of Monge-Ampère Type, Math. U.S.S.R.-Sbornik, Vol. 40, 1981, pp. 179-192. Zbl0467.35020
  11. [11] N.J. Korevaar, An Easy Proof of the Interior Gradient Bound for Solutions to the Prescribed Mean Curvature Problem, Trans. A.M.S. (to appear). Zbl0599.35046
  12. [12] N.V. Krylov, Boundedly Nonhomogeneous Elliptic and Parabolic Equations in a Domain, Izvestia Math. Ser., Vol. 47, 1983, pp. 75-108. Zbl0578.35024MR688919
  13. [13] V.I. Oliker, Hypersurfaces in Rn+1 with Prescribed Gaussian Curvature and Related Equations of Monge-Ampère Type, Comm. Part. Diff. Eqtns., Vol. 9, 1984, pp. 807-838. Zbl0559.58031MR748368
  14. [14] A.V. Pogorelov, The Minkowski Multi-Dimensional Problem, Wiley, New York, 1978. 
  15. [15] L. Simon, Interior Gradient Bounds for Non-Uniformly Elliptic Equations, Indiana U. Math. J., Vol. 25, (9), 1976, pp. 821-855. Zbl0346.35016MR412605
  16. [16] A.E. Treibergs and S.W. Wei, Embedded Hypersurfaces with Prescribed Mean Curvature, J. Diff. Geom., Vol. 18, 1983, pp. 513-521. Zbl0529.53043MR723815
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