Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 24, Number 2 (2020), 483-499.
Boundary Continuity of Nonparametric Prescribed Mean Curvature Surfaces
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.
Taiwanese J. Math., Volume 24, Number 2 (2020), 483-499.
Received: 19 December 2018
Revised: 28 April 2019
Accepted: 8 May 2019
First available in Project Euclid: 16 May 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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