A Liouville-Gelfand Equation for k-Hessian Operators

Authors

Jon T. Jacobsen, Harvey Mudd CollegeFollow

Document Type

Article

Department

Mathematics (HMC)

Publication Date

Summer 2004

Abstract

In this paper we establish existence and multiplicity results for a class of fully nonlinear elliptic equations of k-Hessian type with exponential nonlinearity. In particular, we characterize the precise dependence of the multiplicity of solutions with respect to both the space dimension and the value of k. The choice of exponential nonlinearity is motivated by the classical Liouville-Gelfand problem from combustible gas dynamics and prescribed curvature problems.

Comments

This article is also available from the Rocky Mountain Journal of Mathematics via Project Euclid at http://dx.doi.org/10.1216/rmjm/1181069873.

Rights Information

© 2004 Rocky Mountain Mathematics Consortium

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1216/rmjm/1181069873

Recommended Citation

J. Jacobsen. "A Liouville-Gelfand Equation for k-Hessian Operators," Rocky Mountain J. Math., Vol. 34(2004), No 2, pp. 665-684.