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."
General
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