Table of contents

CONTENTS Introduction § 1. Statement of the problem and of the main theorem § 2. Auxiliary constructions § 3. Ordinary equations and systems § 4. Partial differential equations § 5. Fundamental solutions of regular boundary value problems § 6. Formulae for the fundamental solutions of regular equations References

CONTENTS Introduction Chapter I. Elliptic boundary problems depending on a parameter § 1. The space § 2. Elliptic equations in § 3. Elliptic problems in a half-space § 4. Elliptic problems in a bounded region. Apriori estimates § 5. Elliptic problems in a bounded region. Existence theorem § 6. Generalizations, variants, consequences Chapter II. Mixed parabolic problems § 7. The spaces and § 8. The spaces and § 9. Single-valued solubility of a parabolic mixed problem in the spaces § 10. The case of non-homogeneous initial conditions. Conditions of consistency § 11. Parabolic problems in a finite time interval § 12. Generalization to the case of coefficients depending on time. The case of a parabolic system Supplement. Proof of Lemma 7.1 References