Abstract
This chapter focuses on a priori estimates and Fredholm operators. The basic proposition for interface on the real line is introduced. The proposition is necessary for studying the a priori estimates for operators with constant coefficients in the half-space. A priori estimates in a bounded domain with interfaces are discussed. The a priori estimate for the interface problem defined in two half-spaces is dropped and only the final a priori estimate for an arbitrary bounded domain with interfaces is provided. It is proved that the operator P together with its dual operator P* is Fredholm, which is a substitute for the basic duality principle in linear algebra. A complete description of the set Λl for the operator L = Δp is provided. The main reason for the possibility of providing such a complete description is that the Green formulas for the operator Δp are relatively simple. The case L = Δ2 is also considered in this chapter.
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