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

[AT] C. J. Amick and J. F. Toland, <i>Nonlinear elliptic eigenvalue problems on an infinite strip. Global theory of bifurcation and asymptotic bifurcation</i>, Math. Ann. <b>262</b> (1983), no. 3, 313–342.

[Ba] P. Bauman, <i>Positive solutions of elliptic equations in nondivergence form and their adjoints</i>, Ark. Mat. <b>22</b> (1984), no. 2, 153–173.

[B] H. Berestycki, <i>Le nombre de solutions de certains problèmes semi-linéaires elliptiques</i>, J. Funct. Anal. <b>40</b> (1981), no. 1, 1–29.

[BCN1] H. Berestycki, L. A. Caffarelli, and L. Nirenberg, <i>Uniform estimates for regularization of free boundary problems</i>, 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, <i>Symmetry for elliptic equations in a half space</i>, 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, <i>Monotonicity for elliptic equations in an unbounded Lipschitz domain</i>, in preparation.

[BCN4] H. Berestycki, L. A. Caffarelli, and L. Nirenberg, <i>Inequalities for second-order elliptic equations with applications to unbounded domains. II: Symmetry in infinite strips</i>, preprint.

[BN1] H. Berestycki and L. Nirenberg, <i>Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains</i>, Analysis, Et Cetera ed. P. Rabinowitz, et al., Academic Press, Boston, 1990, pp. 115–164.

[BN2] H. Berestycki and L. Nirenberg, <i>On the method of moving planes and the sliding method</i>, Bol. Soc. Brasil. Mat. (N.S.) <b>22</b> (1991), no. 1, 1–37.

[BNV] H. Berestycki, L. Nirenberg, and S. R. S. Varadhan, <i>The principal eigenvalue and maximum principle for second-order elliptic operators in general domains</i>, Comm. Pure Appl. Math. <b>47</b> (1994), no. 1, 47–92.

[BBT] J. L. Bona, D. K. Bose, and R. E. L. Turner, <i>Finite-amplitude steady waves in stratified fluids</i>, J. Math. Pures Appl. (9) <b>62</b> (1983), no. 4, 389–439 (1984).

[CFMS] L. Caffarelli, E. Fabes, S. Mortola, and S. Salsa, <i>Boundary behavior of nonnegative solutions of elliptic operators in divergence form</i>, Indiana J. Math. <b>30</b> (1981), no. 4, 621–640.

[E] M. Esteban, <i>Nonlinear elliptic problems in strip-like domains. Symmetry of positive vortex rings</i>, Nonlinear Anal. <b>7</b> (1983), no. 4, 365–379.

[GNN] B. Gidas, W. M. Ni, and L. Nirenberg, <i>Symmetry and related properties via the maximum principle</i>, Comm. Math. Phys. <b>6</b> (1981), 883–901.

[GT] D. Gilbarg and N. S. Trudinger, <i>Elliptic Partial Differential Equations of Second Order</i>, 2nd ed., Grundlehren Math. Wiss., vol. 224, Springer-Verlag, Berlin, 1983.

[L] P. L. Lions, <i>The concentration-compactness principle in the calculus of variations. The locally compact case. II</i>, Ann. Inst. H. Poincaré Anal. Non Linéaire <b>1</b> (1984), no. 4, 223–283.

[PW] M. H. Protter and H. F. Weinberger, <i>Maximum Principles in Differential Equations</i>, Prentice-Hall, Englewood Cliffs, N.J., 1967.