Analysis

This chapter introduces the analytical theory of variational inequalities (VIs) and considers issues such as the existence of solutions or their qualitative properties (comparison principles, regularity of solutions, etc.), with a view towards applicability to realistic problems in management science and finance and importantly with a view towards setting the scene for the development of numerical methods for the approximation of VIs. Both the finite and infinite dimensional cases are covered in a self-contained fashion, while all results are applied in detailed fully worked examples to the three model problems introduced in the previous chapter, which are revisited using these results. All analytical tools are introduced essentially from scratch, at a level suitable for the intended audience and are motivated and illustrated with examples.