We consider polynomial spline spaces S r d (4) of degree d and smoothness r deened on triangulations. It is known that for d 3r + 2, S r d (4) possesses a basis of star-supported splines, i.e., splines whose supports are at most the set of triangles surrounding a vertex. Here we extend the theory by showing that for all d 3r + 1, there exist triangulations for which no such bases exist. x1. Int...

We study systems of two elliptic equations, with right-hand sides with general power-like superlinear growth, and left-hand sides which are of Isaac’s or Hamilton-Jacobi-Bellman type (however our results are new even for linear lefthand sides). We show that under appropriate growth conditions such systems have positive solutions in bounded domains, and that all such solutions are bounded in the...

This entry in The New Palgrave Dictionary of Economics, Second Edition, provides a brief overview of equilibrium existence results for continuous and discontinuous non-cooperative games. JEL Classi…cation Number: C7

The amount of information produced in the last decades has grown notably. Much of this information only exists in the form of electronic documents and it has often to be stored for long periods. Therefore, digital archives are increasingly needed. However, for the documents to remain trustworthy while they are archived, they need to be protected by the archivists. Important protection goals tha...

We provide a new class of counter-examples to existence in a simple moral hazard problem in which the first-order approach is valid. In contrast to the Mirrlees example, unbounded likelihood ratios on the signal technology are not central. Rather, our examples center around the behavior of the utility function as utility diverges to negative infinity. For any utility function, such as ln(w), in...