Differential Operators
Yu. M. Berezansky, Zinovij G. Sheftel, Georgij F. Us · Birkhäuser Basel eBooks · 1996
In this chapter, we consider applications of some results of the theory of unbounded operators presented in Chapters 12–15 to the most important class of operators in mathematical physics, namely, to differential operators. For ordinary differential operators, the corresponding applications are described in many books (see, e.g., [AkG, DuS2, LySt, Nai2]); on the other hand, for partial differential equations such results can rarely be found in the literature. In this chapter, the main attention is paid to partial differential equations, namely, to the most important case of elliptic equations. This study requires a fairly complex technique presented in Sections 1 and 2 in sufficiently consistent form. We consider second-order equations (for the case of general order, see, e.g., [Ber]). Note that we do not present the complete spectral theory of elliptic differential operators (for example, we do not study the structure of the spectrum, etc.). The results presented here should be regarded as an illustration of the general theorems on important examples. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.