Let me begin by explaining the meaning of the title of this book. In
essence, the book studies boundary value problems for linear partial
differ- ential equations in a finite domain in n-dimensional Euclidean
space. The problem that is investigated is the question of the
dependence of the nature of the solvability of a given equation on the
way in which the boundary conditions are chosen, i.e. on the
supplementary requirements which the solution is to satisfy on specified
parts of the boundary. The branch of mathematical analysis dealing with
the study of boundary value problems for partial differential equations
is often called mathematical physics. Classical courses in this subject
usually consider quite restricted classes of equations, for which the
problems have an immediate physical context, or generalizations of such
problems. With the expanding domain of application of mathematical
methods at the present time, there often arise problems connected with
the study of partial differential equations that do not belong to any of
the classical types. The elucidation of the correct formulation of these
problems and the study of the specific properties of the solutions of
similar equations are closely related to the study of questions of a
general nature.