Lecture Notes on Mixed Type Partial Differential Equations

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World Scientific, 1990 - Mathematics - 144 pages
This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense. Some of the latest results of the author are also presented in this book.
 

Contents

The dynamical equation of mixed type
1
The Tricomi problem
6
Regularity of solutions in the sense of Tricomi
8
Fundamental idea of Tricomi
9
The BitsadzeLavrentjev problem
33
The Gellerstedt problem
41
The Frankl problem
43
Quasiregularity of solutions in the sense of Protter
54
The a b c energy integral method
55
Weak or strong solutions in the classical sense
86
Wellposedness
123
Open problems
137
Basic Books
138
Subject Index
139
Author Index
143

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