Nagoya Mathematical Journal

On the Dirichlet problem of prescribed mean curvature equations without $H$-convexity condition

Kazuya Hayasida and Masao Nakatani

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Abstract

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.

Article information

Source
Nagoya Math. J., Volume 157 (2000), 177-209.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631349

Mathematical Reviews number (MathSciNet)
MR1752481

Zentralblatt MATH identifier
0965.35068

Subjects
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.

Citation

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


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