IJPAM: Volume 24, No. 2 (2005)

INNER OBSTACLE PROBLEM: CONVERGENCE OF
THE SOLUTIONS FOR IMPEDIMENTS WITH
VARYING DOMAINS

S\lawomir Jagodzinski$^1$, Anna Olek$^2$, Kuba Szczepaniak$^3$
$^{1,2,3}$Centre of Mathematics and Physics
Technical University of \Lódz
al. Politechniki 11, \Lódz, PL-90-924, POLAND
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^3$e-mail: [email protected]


Abstract.In this paper we consider the sequence of the inner obstacle problems. Assuming the convergence of impediments (in certain sense) we obtain strong convergence in $H^1_0(\Omega)$ of the solutions to the solution of the limit inner obstacle problem. It is worth pointing out that this result represents an extension of [#!OS!#], where the sequence of global problems has been considered.

Received: September 1, 2005

AMS Subject Classification: 49J40, 35B65

Key Words and Phrases: inner obstacle problems, variational inequalities

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 24
Issue: 2