Elliptic equations with singular lower order terms

Abstract

The classical theory of elliptic equations assumes that the lower order terms are all bounded (or are in some $L^p$-space with $p$ sufficiently large). In this talk, we examine equations with singular lower order terms. Although some elements of the classical theory can be carried over to this case, several interesting new phenomena occur. In some cases, the equation has only one bounded solution in a given bounded domain. In other cases, there are solutions for arbitrary Dirichlet data but only one smooth solution.