Completeness theorems related to BVPs satisfying the Lopatinskii condition for higher order elliptic equations

Authors : Alberto Cialdea, Flavia Lanzara

Pages : 129-141

Doi:10.33205/cma.1540457

View : 17 | Download : 21

Publication Date : 2024-12-16

Article Type : Research Paper

Abstract :In this paper, we consider a linear elliptic operator $E$ with real constant coefficients of order $2m$ in two independent variables without lower order terms. For this equation, we consider linear BVPs in which the boundary operators $T_1,\\\\ldots,T_m$ are of order $m$ and satisfy the Lopatinskii-Shapiro condition with respect to $E$. We prove boundary completeness properties for the system $\\\\{(T_1\\\\omega_k,\\\\ldots, T_m\\\\omega_k)\\\\}$, where $\\\\{\\\\omega_k\\\\}$ is a system of polynomial solutions of the equation $Eu=0$.
Keywords : Completeness theorems, Lopatinskii condition, Elliptic equations of higher order, Partial differential equations with constant coefficients