Boundary Value Problems Connected with the Newton Polygon

L. R. Volevich, R. Denk


Abstract: In this paper we study boundary value problems for pencils of differential operators depending polynomially on a parameter $\lambda$. The symbols of these pencils for large values of the parameter admit a two-sided estimate formulated in terms of the Newton polygon. We formulate an analog of the Agmon-Agranovich-Vishik condition, which guarantees the existence of the inverse operator in special parameter-depended norms for large $\lambda$. For simplicity we consider only the case of operators with constant coefficients in the half-space. The case of operators with variable coefficients on a manifold with boundary will be treated separately.