Essential spectrum of elliptic systems of pseudo-differential operators on L-2(R-N) circle plus L-2(R-N)

摘要

Inspired by a result of Wong (Partial Differ Equ 13(10):1209-1221, 1988), we establish an analytic description of the essential spectrum of non-self-adjoint mixed-order systems of pseudo-differential operators on L-2(R-N) circle plus L-2(R-N) that are uniformly Douglis-Nirenberg elliptic with positive-order diagonal entries. We apply our result to a problem arising in the dynamics of falling liquid films.