Parameter dependent pseudodifferential boundary value problems and their applications to trace asymptotics and eta-invariants.

Agranovich and Vishik constructed a theory of elliptic boundary value problems depending on a parameter $p\in \mathbb{R}$. This theory plays an important role in the study of many classes of differential equations and their applications (for example, in the case of equations on manifolds with singularities). We report about an analogue of this theory in the case of boundary value problems for pseudodifferential operators. As applications, we will obtain trace asymptotics for elliptic problems with a parameter as $p\to\infty$ and define $\eta$-invariants for elliptic problems with a parameter.
The results were obtained in collaboration with K.N. Zhuikov.