Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of
physics and geometry including fluid and plasma dynamics optics cosmology traffic
engineering projective geometry geometric variational theory and the theory of isometric
embeddings. And yet even the linear theory of these equations is at a very early stage. This
text examines various Dirichlet problems which can be formulated for equations of Keldysh type
one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions
(in which data are prescribed on only part of the boundary) and closed boundary conditions (in
which data are prescribed on the entire boundary) are both considered. Emphasis is on the
formulation of boundary conditions for which solutions can be shown to exist in an appropriate
functions space. Specific applications to plasma physics optics and analysis on projective
spaces are discussed. (From the preface)
