Speaker
Dr
Hayk Mikayelyan
(University of Nottingham Ningbo China)
Description
Consider the cylindrical domain $\Omega=D\times(0,1)$ and the convex functional
$$
\int_\Omega \frac{1}{2}|\nabla U(x)|^2dx +\int_D V(x')^+\,dx',
$$
with nonlocal obstacle acting on function $V(x')=\int_0^1 U(x', t) dt $.
We show that the unique minimizer solves the equation
$$
\Delta U(x',x_n) = \chi_{\{V>0\}}(x') + \chi_{\{V=0\}}(x') [\partial_\nu U (x',0) + \partial_\nu U (x',1)],
$$
where $\partial_\nu U$ is the exterior normal derivative of $U$.
Several further regularity results are proven. It is shown that the comparison principle does not hold for minimizers, which makes numerical approximation somewhat challenging.
Author
Dr
Hayk Mikayelyan
(University of Nottingham Ningbo China)