Abstract
The influence of the geometry of the domain on the behavior of generalized solutions of Dirichlet problems for elliptic partial differential equations has been an important subject for over a century. We investigate the boundary behavior of variational solutions $f$ of Dirichlet problems for prescribed mean curvature equations in a domain $\Omega \subset \mathbb{R}^{2}$ near a point $\mathcal{O} \in \partial \Omega$ under different assumptions about the curvature of $\partial \Omega$ on each side of $\mathcal{O}$. We prove that the radial limits at $\mathcal{O}$ of $f$ exist under different assumptions about the Dirichlet boundary data $\phi$, depending on the curvature properties of $\partial \Omega$ near $\mathcal{O}$.
Funding Statement
This research partially supported by NSF Award
HRD-1824267.
Acknowledgments
The authors would like to thank the referee for his/her efforts.
Citation
Mozhgan Nora Entekhabi. Kirk Eugene Lancaster. "Radial Limits of Nonparametric PMC Surfaces with Intermediate Boundary Curvature." Taiwanese J. Math. 25 (3) 599 - 613, June, 2021. https://doi.org/10.11650/tjm/201101
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