Electron. J. Diff. Equ.,
Vol. 2016 (2016), No. 105, pp. 111.
Optimization problems on the Sierpinski gasket
Marek Galewski
Abstract:
We investigate the existence of an optimal process for such an optimal
control problem in which the dynamics is given by the Dirichlet problem
driven by weak Laplacian on the Sierpinski gasket. To accomplish this task
using a direct variational approach with no global growth conditions on the
nonlinear term, we consider the existence of solutions, their uniqueness and
their dependence on a functional parameter for mentioned Dirichlet problem.
This allows us to prove that the optimal control problem admits at least
one solution.
Submitted January 18, 2016. Published April 22, 2016.
Math Subject Classifications: 35J20, 28A80, 49J20.
Key Words: Control problem; Sierpinski gasket; direct variational method;
continuous dependence on parameters.
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Marek Galewski
Institute of Mathematics
Lodz University of Technology
Wolczanska 215, 90924 Lodz, Poland
email: marek.galewski@p.lodz.pl

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