Differential and Integral Equations

Spacelike graphs with prescribed mean curvature

Marie Françoise Bidaut-Veron and Andrea Ratto

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We describe all the rotationally symmetric spacelike graphs $G_u=\bigl( x,u(\vert x\vert)\bigr)$ in Minkowsky's space whose mean curvature is a prescribed function $f$ of $u$. In particular, we prove the existence of regular and singular solutions by means of a fixed-point theorem, and we study the global behaviour of solutions in the case $f(u)\cdot u$ does not change sign.

Article information

Differential Integral Equations, Volume 10, Number 5 (1997), 1003-1017.

First available in Project Euclid: 1 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 35J60: Nonlinear elliptic equations


Bidaut-Veron, Marie Françoise; Ratto, Andrea. Spacelike graphs with prescribed mean curvature. Differential Integral Equations 10 (1997), no. 5, 1003--1017. https://projecteuclid.org/euclid.die/1367438630

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