Regular Elliptic Differential Equations

Abstract

Let Ω be a bounded C ^∞-domain in R _n with boundary ∂Ω. Let A,

$$(Au)(x) = \sum\limits_{\left| \alpha \right|\underline{\underline < } 2m} {a_\alpha (x)D^\alpha u(x), x \in \overline \Omega },$$

((1))

be a properly elliptic differential operator in $\bar \Omega$, and let $B_1,\ldots ,B_m,$

$$(B_j u)(y) = \sum\limits_{\left| \alpha \right|\underline{\underline < } m_j } {b_{j,\alpha } (y)D^\alpha u(y),\,y \in \partial \Omega, }$$

((2))

be m boundary operators such that $\left\{ {A;\,B_1 ,...,B_m } \right\}$ is regular elliptic (of. the definition in 4.1.2.).