 |
 |
 |
 |
 |
|
|
Arie Leizarowitz, Technion, Israel"On second order two-dimensional variational problems on unbounded domains" Abstract
We consider the energy functional
![\begin{displaymath}J_{\Omega }=\int _{\Omega }[(\Delta u)^2-b\vert\nabla u\vert^2+\psi (u)]dxdy\end{displaymath}](img1.png){kind=small}
where  is a bounded domain in 
and  is a  super
quadratic potential. Associated with this functional is the notion of mean
energy, which is meaningful for a class of configurations  on the whole
plane, and we study the corresponding minimization problem. Minimizers of
this problem are called equilibrium configurations. We establish
apriori bounds for this unbounded-domain problem, and use it to establish
existence of equilibrium configurations.
We also discuss the existence of radially symmetric equilibrium
configurations. Moreover, we remark on the connection between radially
symmetric configurations and 1-dimensional configurations.
TUESDAY, October 10, 2000 |
|
|
|
|
|
|