ELLIPTIC PROBLEMS WITH A PARAMETER AND PARABOLIC PROBLEMS OF GENERAL TYPE

Abstract

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