## Journal of the Mathematical Society of Japan

- J. Math. Soc. Japan
- Volume 56, Number 4 (2004), 1169-1201.

### Dirichlet problem for evolutionary surfaces of prescribed mean curvature in a non-convex domain

Kazuya HAYASIDA and Yoshiaki IKEDA

#### Abstract

We show the existence of solutions for Dirichlet problem of evolutionary surfaces of prescribed mean curvature. Usually the lateral boundary needs to satisfy a kind of convexity, more precisely $H$-convexity condition. But in this article we do not assume it on a portion $S$ of the lateral boundary. Under some assumptions on the exterior forces and the shape of $S$ we prove that the solution satisfies Dirichlet boundary condition on $S$ in a weak sense.

#### Article information

**Source**

J. Math. Soc. Japan, Volume 56, Number 4 (2004), 1169-1201.

**Dates**

First available in Project Euclid: 27 September 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.jmsj/1190905454

**Digital Object Identifier**

doi:10.2969/jmsj/1190905454

**Mathematical Reviews number (MathSciNet)**

MR2092943

**Zentralblatt MATH identifier**

1063.35078

**Subjects**

Primary: 35K55: Nonlinear parabolic equations

Secondary: 35K20: Initial-boundary value problems for second-order parabolic equations

**Keywords**

Dirichlet problem evolutionary surfaces of prescribed mean curvature boundary mean curvature

#### Citation

HAYASIDA, Kazuya; IKEDA, Yoshiaki. Dirichlet problem for evolutionary surfaces of prescribed mean curvature in a non-convex domain. J. Math. Soc. Japan 56 (2004), no. 4, 1169--1201. doi:10.2969/jmsj/1190905454. https://projecteuclid.org/euclid.jmsj/1190905454