Unilateral Problems for Scalar Functions
In this chapter we will consider boundary-value problems with one-sided conditions in the form of inequalities, where the unknown is a single real scalar function in a given domain of an n-dimensional space R n, n = 2, 3. First we pay attention to problems in which the inequalities are prescribed only on the boundary of the domain considered. Then we deal with problems which involve inequalities inside the domain, i.e., with an obstacle inside the domain. For the sake of simplicity we restrict our exposition to the second order elliptic operators.
Unable to display preview. Download preview PDF.