Duke Mathematical Journal

Inequalities for second-order elliptic equations with applications to unbounded domains I

H. Berestycki, L. A. Caffarelli, and L. Nirenberg

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J., Volume 81, Number 2 (1996), 467-494.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077245673

Digital Object Identifier
doi:10.1215/S0012-7094-96-08117-X

Mathematical Reviews number (MathSciNet)
MR1395408

Zentralblatt MATH identifier
0860.35004

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B45: A priori estimates

Citation

Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. Inequalities for second-order elliptic equations with applications to unbounded domains I. Duke Math. J. 81 (1996), no. 2, 467--494. doi:10.1215/S0012-7094-96-08117-X. https://projecteuclid.org/euclid.dmj/1077245673


Export citation

References

  • [AT] C. J. Amick and J. F. Toland, Nonlinear elliptic eigenvalue problems on an infinite strip. Global theory of bifurcation and asymptotic bifurcation, Math. Ann. 262 (1983), no. 3, 313–342.
  • [Ba] P. Bauman, Positive solutions of elliptic equations in nondivergence form and their adjoints, Ark. Mat. 22 (1984), no. 2, 153–173.
  • [B] H. Berestycki, Le nombre de solutions de certains problèmes semi-linéaires elliptiques, J. Funct. Anal. 40 (1981), no. 1, 1–29.
  • [BCN1] H. Berestycki, L. A. Caffarelli, and L. Nirenberg, Uniform estimates for regularization of free boundary problems, Analysis and Partial Differential Equations ed. C. Sadosky, Lecture Notes in Pure and Appl. Math., vol. 122, Dekker, New York, 1990, pp. 567–619.
  • [BCN2] H. Berestycki, L. A. Caffarelli, and L. Nirenberg, Symmetry for elliptic equations in a half space, Boundary Value Problems for Partial Differential Equations and Applications ed. J. L. Lions, et al., RMA Res. Notes Appl. Math., vol. 29, Masson, Paris, 1993, pp. 27–42.
  • [BCN3] H. Berestycki, L. A. Caffarelli, and L. Nirenberg, Monotonicity for elliptic equations in an unbounded Lipschitz domain, in preparation.
  • [BCN4] H. Berestycki, L. A. Caffarelli, and L. Nirenberg, Inequalities for second-order elliptic equations with applications to unbounded domains. II: Symmetry in infinite strips, preprint.
  • [BN1] H. Berestycki and L. Nirenberg, Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains, Analysis, Et Cetera ed. P. Rabinowitz, et al., Academic Press, Boston, 1990, pp. 115–164.
  • [BN2] H. Berestycki and L. Nirenberg, On the method of moving planes and the sliding method, Bol. Soc. Brasil. Mat. (N.S.) 22 (1991), no. 1, 1–37.
  • [BNV] H. Berestycki, L. Nirenberg, and S. R. S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math. 47 (1994), no. 1, 47–92.
  • [BBT] J. L. Bona, D. K. Bose, and R. E. L. Turner, Finite-amplitude steady waves in stratified fluids, J. Math. Pures Appl. (9) 62 (1983), no. 4, 389–439 (1984).
  • [CFMS] L. Caffarelli, E. Fabes, S. Mortola, and S. Salsa, Boundary behavior of nonnegative solutions of elliptic operators in divergence form, Indiana J. Math. 30 (1981), no. 4, 621–640.
  • [E] M. Esteban, Nonlinear elliptic problems in strip-like domains. Symmetry of positive vortex rings, Nonlinear Anal. 7 (1983), no. 4, 365–379.
  • [GNN] B. Gidas, W. M. Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 6 (1981), 883–901.
  • [GT] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Grundlehren Math. Wiss., vol. 224, Springer-Verlag, Berlin, 1983.
  • [L] P. L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. II, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), no. 4, 223–283.
  • [PW] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, N.J., 1967.