Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 157 (2000), 177-209.
On the Dirichlet problem of prescribed mean curvature equations without $H$-convexity condition
The Dirichlet problem of prescribed mean curvature equations is well posed, if the boundery is H-convex. In this article we eliminate the H-convexity condition from a portion $\Gamma$ of the boundary and prove the existence theorem, where the boundary condition is satisfied on $\Gamma$ in the weak sense.
Nagoya Math. J., Volume 157 (2000), 177-209.
First available in Project Euclid: 27 April 2005
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J60: Nonlinear elliptic equations
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 58E15: Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.
Hayasida, Kazuya; Nakatani, Masao. On the Dirichlet problem of prescribed mean curvature equations without $H$-convexity condition. Nagoya Math. J. 157 (2000), 177--209. https://projecteuclid.org/euclid.nmj/1114631349