Vol. 88, No. 2, 1980

Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Height estimates for exterior problems of capillarity type

Bruce Edward Turkington

Vol. 88 (1980), No. 2, 517–540

This work concerns boundary value problems for a class of nonlinear equations modeled on the physical equations for a capillary free surface in a gravitational field. The results consist principally of estimates for the height of a solution in an exterior domain. Structure conditions reflecting the nonlinearity of the mean curvature operator are imposed on a class of symmetric variational operators in terms of the Legendre transform of the variational integrand. Estimates are found for the boundary height of a rotationally symmetric solution in the exterior of a ball of radius R. These estimates, which are valid for any R, are shown to be asymptotically exact as R tends to zero or infinity. This provides a proof of the asymptotic behavior of the boundary height which previously has been derived by a formal perturbation method. An asymptotic characterization of the solution in a neighborhood of the boundary is also given. For a general domain estimates are obtained from a maximum principle due to Finn in which the symmetric solutions serve as comparison functions.

Mathematical Subject Classification 2000
Primary: 35J65
Secondary: 49F10
Received: 28 March 1979
Published: 1 June 1980
Bruce Edward Turkington