Taiwanese Journal of Mathematics

Boundary Continuity of Nonparametric Prescribed Mean Curvature Surfaces

Mozhgan Nora Entekhabi and Kirk E. Lancaster

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Abstract

We investigate the boundary behavior of variational solutions of Dirichlet problems for prescribed mean curvature equations at smooth boundary points where certain boundary curvature conditions are satisfied (which preclude the existence of local barrier functions). We prove that if the Dirichlet boundary data $\phi$ is continuous at such a point (and possibly nowhere else), then the solution of the variational problem is continuous at this point.

Article information

Source
Taiwanese J. Math., Advance publication (2019), 17 pages.

Dates
First available in Project Euclid: 16 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1557972013

Digital Object Identifier
doi:10.11650/tjm/190504

Subjects
Primary: 35J67: Boundary values of solutions to elliptic equations
Secondary: 35J93: Quasilinear elliptic equations with mean curvature operator 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Keywords
prescribed mean curvature Dirichlet problem boundary continuity

Citation

Entekhabi, Mozhgan Nora; Lancaster, Kirk E. Boundary Continuity of Nonparametric Prescribed Mean Curvature Surfaces. Taiwanese J. Math., advance publication, 16 May 2019. doi:10.11650/tjm/190504. https://projecteuclid.org/euclid.twjm/1557972013


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