Equations of the Mixed Type

Foreword

Introduction


1. General Remarks on Linear Partial Differential Equations of Mixed Type


1. Equation of the Second Order with Two Independent Variables


2. The Theory of Cibrario


3. Systems of Two First Order Equations


4. Linear Systems of Partial Differential Equations of the Second Order with Two Independent Variables


2. The Study of the Solutions of Second Order Hyperbolic Equations with Initial Conditions Given along the Lines of Parabolicity


1. The Riemann Function for a Second Order Hyperbolic Linear Equation


2. A Class of Hyperbolic Systems of Second Order Linear Equations


3. The Cauchy Problem for Hyperbolic Equations with Given Initial Conditions on the Line of Parabolic Degeneracy


4. Generalizations


3. The Study of the Solutions of Second Order Elliptic Equations for a Domain, the Boundary of Which Includes a Segment of the Curve of Parabolic Degeneracy


1. The Linear Elliptic Partial Differential Equation of the Second Order


2. Elliptic Systems of Second Order


3. The Dirichlet Problem for Second Order Elliptic Equations in a Domain, the Boundary of Which Includes a Segment of the Curve of Parabolic Degeneracy


4. Some other Problems and Generalizations


4. The Problem of Tricomi


1. The Statement of the Problem of Tricomi


2. The Extremal Principle and the Uniqueness of the Solution of Problem Τ


3. Solution of Problem Τ by Means of the Method of Integral Equations


4. Continuation: The Proof for the Existence of a Solution of the Integral Equations Obtained in the Preceding Paragraph


5. Other Methods for Solving Problem Τ


6. Examples and Generalizations


5. Other Mixed Problems


1. The Mixed Problem Μ


2. The Proof of the Uniqueness of Solution for Problem Μ


3. Concerning the Existence of the Solution of Problem Μ


4. The General Mixed Problem


5. The Problem of Frankl


6. Short Indication of some Important Generalizations and Applications

References

Index