To summarize briefly, this book is devoted to an exposition of the
foundations of pseudo differential equations theory in non-smooth
domains. The elements of such a theory already exist in the
literature and can be found in such papers and monographs as
[90,95,96,109,115,131,132,134,135,136,146,
163,165,169,170,182,184,214-218]. In this book, we will employ a
theory that is based on quite different principles than those used
previously. However, precisely one of the standard principles is
left without change, the "freezing of coefficients" principle. The
first main difference in our exposition begins at the point when
the "model problem" appears. Such a model problem for differential
equations and differential boundary conditions was first studied in
a fundamental paper of V. A. Kondrat'ev [134]. Here also the second
main difference appears, in that we consider an already given
boundary value problem. In some transformations this boundary value
problem was reduced to a boundary value problem with a parameter .
-\ in a domain with smooth boundary, followed by application of the
earlier results of M. S. Agranovich and M. I. Vishik. In this
context some operator-function R('-\) appears, and its poles
prevent invertibility; iffor differential operators the function is
a polynomial on A, then for pseudo differential operators this
dependence on . -\ cannot be defined. Ongoing investigations of
different model problems are being carried out with approximately
this plan, both for differential and pseudodifferential boundary
value problems.
General
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