## Taiwanese Journal of Mathematics

### Boundary Continuity of Nonparametric Prescribed Mean Curvature Surfaces

#### 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., Volume 24, Number 2 (2020), 483-499.

Dates
Revised: 28 April 2019
Accepted: 8 May 2019
First available in Project Euclid: 16 May 2019

https://projecteuclid.org/euclid.twjm/1557972013

Digital Object Identifier
doi:10.11650/tjm/190504

Mathematical Reviews number (MathSciNet)
MR4078207

Zentralblatt MATH identifier
07192944

#### Citation

Entekhabi, Mozhgan Nora; Lancaster, Kirk E. Boundary Continuity of Nonparametric Prescribed Mean Curvature Surfaces. Taiwanese J. Math. 24 (2020), no. 2, 483--499. doi:10.11650/tjm/190504. https://projecteuclid.org/euclid.twjm/1557972013

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