Duke Mathematical Journal

Qualitative properties of solutions to some nonlinear elliptic equations in $R^2$

Wenxiong Chen and Congming Li

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 71, Number 2 (1993), 427-439.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077290061

Digital Object Identifier
doi:10.1215/S0012-7094-93-07117-7

Mathematical Reviews number (MathSciNet)
MR1233443

Zentralblatt MATH identifier
0923.35055

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 53A30: Conformal differential geometry 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

Citation

Chen, Wenxiong; Li, Congming. Qualitative properties of solutions to some nonlinear elliptic equations in R 2 . Duke Math. J. 71 (1993), no. 2, 427--439. doi:10.1215/S0012-7094-93-07117-7. http://projecteuclid.org/euclid.dmj/1077290061.


Export citation

References

  • [1] W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991), no. 3, 615–622.
  • [2] J. Kazdan and F. Warner, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math. 28 (1975), no. 5, 567–597.
  • [3] J. Bebernes and D. Eberly, Mathematical Problems from Combustion Theory, Appl. Math. Sci., vol. 83, Springer-Verlag, New York, 1989.
  • [4] K. Cheng and W. Ni, On the structure of the conformal Gaussian curvature equation on $\bf R\sp 2$, Duke Math. J. 62 (1991), no. 3, 721–737.
  • [5] W. Ni, On the elliptic equation $\Delta u+K(x)e\sp2u=0$ and conformal metrics with prescribed Gaussian curvatures, Invent. Math. 66 (1982), no. 2, 343–352.
  • [6] R. McOwen, Conformal metrics in $\mathbf R^2$ with prescribed Gaussian curvature and positive total curvature, Indiana Univ. Math. J. 34 (1985), no. 1, 97–104.
  • [7] P. Aviles, Conformal complete metrics with prescribed nonnegative Gaussian curvature in $\bf R\sp 2$, Invent. Math. 83 (1986), no. 3, 519–544.
  • [8] J. Kazdan and F. Warner, Curvature functions for compact $2$-manifolds, Ann. of Math. (2) 99 (1974), 14–47.
  • [9] C. Li, Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains, Comm. Partial Differential Equations 16 (1991), no. 4-5, 585–615.
  • [10] H. Brezis and F. Merle, Uniform estimates and blow-up behavior for solutions of $\Delta u=v(x) \exp u(x)$ in two dimensions, preprint.