Vol. 88, No. 2, 1980

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ISSN: 0030-8730
Height estimates for capillary surfaces

David Siegel

Vol. 88 (1980), No. 2, 471–515
Abstract

In this paper estimates are obtained for any scalar function u(x) that staisfies the equation

div(T u) = κu  in Ω
(1a)

and the boundary condition

Tu ⋅ν = cosγ  on Σ = dΩ.
(1b)

Here κ is a positive constant, Ω is an open domain in n-dimensional Euclidean space, ν is the exterior unit normal on Σ, and Tu is the vector operator
          1
T u = ∘--------2∇u.
1+ |∇u |

Mathematical Subject Classification 2000
Primary: 35J65
Milestones
Received: 28 September 1979
Published: 1 June 1980
Authors
David Siegel
Applied Mathematics
University of Waterloo
200 University Ave West
Waterloo N2L 3G1
Canada
http://www.math.uwaterloo.ca/~dsiegel/