Partial Differential Equations

1. Front Matter

   Pages I-XII

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2. Elements of Spectral Theory

   • Aleksei A. Dezin

   Pages 1-23

3. Function Spaces and Operators Generated by Differentiation

   • Aleksei A. Dezin

   Pages 24-54

4. Ordinary Differential Operators

   • Aleksei A. Dezin

   Pages 55-68

5. Model Operators

   • Aleksei A. Dezin

   Pages 69-80

6. First-Order Operator Equations

   • Aleksei A. Dezin

   Pages 81-104

7. Operator Equations of Higher Order

   • Aleksei A. Dezin

   Pages 105-118

8. General Existence Theorems for Proper Operators

   • Aleksei A. Dezin

   Pages 119-130

9. A Special Operational Calculus

   • Aleksei A. Dezin

   Pages 131-143

10. Concluding Remarks

    • Aleksei A. Dezin

    Pages 144-145

11. Back Matter

    Pages 146-165

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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.

• Boundary value problem
• differential equation
• mathematical analysis
• partial differential equation

• Steklov Mathematical Institute, Moscow, USSR

  Aleksei A. Dezin

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