Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Advance publication (2019), 17 pages.
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., Advance publication (2019), 17 pages.
First available in Project Euclid: 16 May 2019
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Digital Object 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., advance publication, 16 May 2019. doi:10.11650/tjm/190504. https://projecteuclid.org/euclid.twjm/1557972013