## Journal of the Mathematical Society of Japan

### A semilinear elliptic equation in a thin network-shaped domain

Satoshi KOSUGI

#### Abstract

We consider a semilinear elliptic equation in a varying thin domain of $R^{n}$. This thin domain degenerates into a geometric graph when a certain parameter tends to zero. We determine a limit equation on the graph and we prove that a solution of the PDE converges to a solution of the limit equation. Conversely, when a solution of the limit equation is given, we construct a solution of the PDE approaching a solution of the limit equation.

#### Article information

Source
J. Math. Soc. Japan, Volume 52, Number 3 (2000), 673-697.

Dates
First available in Project Euclid: 10 June 2008

https://projecteuclid.org/euclid.jmsj/1213107294

Digital Object Identifier
doi:10.2969/jmsj/05230673

Mathematical Reviews number (MathSciNet)
MR1760612

Zentralblatt MATH identifier
0961.35050

Subjects
Primary: 35J60: Nonlinear elliptic equations

#### Citation

KOSUGI, Satoshi. A semilinear elliptic equation in a thin network-shaped domain. J. Math. Soc. Japan 52 (2000), no. 3, 673--697. doi:10.2969/jmsj/05230673. https://projecteuclid.org/euclid.jmsj/1213107294