In this paper pencils of partial differential operators depending polynomially on a complex parameter and corresponding boundary value problems with general boundary conditions are studied. We define a concept of ellipticity for such problems (for which the parameter-dependent symbol in general is not quasi-homogeneous) in terms of the Newton polygon and introduce related parameter-dependent norms. It is shown that this type of ellipticity leads to unique solvability of the boundary value problem and to two-sided a priori estimates for the solution.
"Parameter-elliptic boundary value problems connected with the Newton polygon." Differential Integral Equations 15 (3) 289 - 326, 2002. https://doi.org/10.57262/die/1356060862