An optimal control problem for some nonlinear elliptic equations with unbounded coefficients
An optimal control problem for some nonlinear elliptic equations with unbounded coefficients
We study an optimal control problem associated to a Dirichlet boundary value problem of the type \begin{document}$ \begin{equation*} \mbox{(BVP) }\,\,\,\,\,\,\,\, {\rm{div}}\; \left[ \beta(x)\nabla u (x) + \left( A\frac {x}{|x|^2 } +g(x) \right)u(x)\right] = {\rm{div}}\; \mathcal F,\quad u\in W^{1,p}_0( \Omega ) , \end{equation*} $\end{document} $ 1<p\leqslant 2, $ where $ \Omega …