On approximation of an optimal boundary control problem for linear elliptic equation with unbounded coefficients (Q379867)

Based on the author's abstract: The paper deals with an Optimal boundary Control Problem (OCP) associated to a linear elliptic equation NEWLINE\[NEWLINE -\mathrm{div}(\nabla y + A(x)\nabla y)=f,NEWLINE\]NEWLINE where the matrix \(A=(a_{i\,j})\) is skew-symmetric, \(a_{i\,j}(x)=-a_{j\,i}(x)\), measurable and belongs to \(L^2\). It is observed that an optimal solution to such problem can inherit the singular character of the matrix \(A\). The author studies the existence of an optimal solution to a boundary problem related with this type of equation and in particular considers two types of optimal solutions, the so-called variational and non-variational solutions, and proves that each of that optimal solutions can be attainable by solutions of special optimal boundary control problems.