Category:Elliptic

This category contains all control problems which are governed by an elliptic partial differential equation.

A second order linear partial differential equation can be written as

 $\sum^n_{i,j=1} a_{i,j} \frac{\partial^2}{\partial x_i \partial x_j} +\quad \textrm{ lower-order terms} = 0$ .

If  $A=(a_{i,j})_{i,j}$  is positive or negative definite, the partial differential equation is called elliptic.

An example is the Poisson's equation:  $-\Delta u = f$ ,
where  $\Delta$  denotes the Laplace operator,  $u$  is the unknown, and the function  $f$  given.