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June, 2021 Radial Limits of Nonparametric PMC Surfaces with Intermediate Boundary Curvature
Mozhgan Nora Entekhabi, Kirk Eugene Lancaster
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Taiwanese J. Math. 25(3): 599-613 (June, 2021). DOI: 10.11650/tjm/201101

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

Download 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

Information

Received: 23 July 2020; Revised: 9 November 2020; Accepted: 12 November 2020; Published: June, 2021
First available in Project Euclid: 30 November 2020

Digital Object Identifier: 10.11650/tjm/201101

Subjects:
Primary: 35J67
Secondary: 35J93, 53A10

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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