UID:
almahu_9947367001402882
Format:
1 online resource (515 p.)
ISBN:
1-282-28970-5
,
9786612289705
,
0-08-095554-1
Series Statement:
Mathematics in science and engineering ; v. 46
Uniform Title:
Lineĭnye i kvazilineĭnye uravnenii͡a ėllipticheskogo tipa.
Content:
Linear and quasilinear elliptic equations
Note:
Translation of [Lineinye i kvazilineinye uravneniia ellipticheskogo tipa].
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Front Cover; Linear and Quasilinear Elliptic Equations; Copyright Page; Contents; Preface; CHAPTER 1. INTRODUCTION; 1. The Basic Notation and Terminology; 2. Admissible Extensions of the Concept of Solution of Linear and Quasilinear Equations; 3. The Basic Results and Their Possible Development; CHAPTER 2. AUXILIARY PROPOSITIONS; 1. Some Simple Inequalities; 2. Functions in the Class Wlm (O); 3. Functions in the Classes Wlm (O) and Wlm (O); 4. Other Auxiliary Propositions; 5. Bounds for max |u(x)|; 6. The Function Class Bm (O,M,?,d,1/q); 7. The Classes Bm (OUS1,...) and Bm (OUS1,...)
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8. The Classes BmN1CHAPTER 3. LINEAR EQUATIONS; 1. Solvability of the Dirichlet Problem in the Spaces Cl,a(O), l〉=2; 2. Schauder's A Priori Estimate; 3. The Solvability in C2,a(O) of Other Boundary-Value Problems; 4. Generalized Solutions in w12 (O) The First Fundamental Inequality; 5. Solvability of the First Boundary-Value Problem in W12(O); 6. The Second and Third Boundary-Value Problems; 7. Interior Estimates in L2 of the Second Derivatives of an Arbitrary Function in Terms of the Values of an Elliptic Operator Applied to It; 8. The Second Fundamental Inequality for Elliptic Operators
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9. On the Solvability of the First Boundary-Value Problem in the Space W22, 0 (O)10. Conditions Under Which Generalized Solutions in W12(O) Belong to W22 (O); 11. Other Ways of Proving the Second Fundamental Inequality; 12. Conditions Under Which Generalized Solutions in W22 Belong to Cl,a for l〉=2; 13. The Boundedness of Generalized Solutions in W12 (O); 14. Conditions Under Which Generalized Solutions in W12 (O) Belong to C0,a; 15. Conditions for Boundedness of max I ?u| and I uxla for Generalized Solutions in W12 (O); 16. Diffraction Problems; 17. The Case of Two Independent Variables
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18. Two-Dimensional Saddle-Shaped SurfacesCHAPTER 4. QUASILINEAR EQUATIONS WITH PRINCIPAL PART IN DIVERGENCE FORM; 1. Bounded Generalized Solutions. Continuity in the Sense of Holder; 2. Uniqueness in the Small; 3. A Bound for max O |?u|; 4. A Bound for max |?u| Over the Entire Region O; 5. Generalized Second-Order Derivatives; 6. A Bound for the Norms |u|l,a' Where l〉=1; 7. Bounds for the Maximum Absolute Values of Generalized Solutions; 8. Existence Theorems; CHAPTER 5. VARIATIONAL PROBLEMS; 1. Statement of the Problems; 2. Finding Functions That Minimize the Functional l (u)
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3. Finding a Bound for the Maximum Absolute Value of Solutions of Variational Problems4. Proof of Hölderness of Generalized Solutions; 5. The Theorem on Uniqueness in the Small of Generalized Solutions; 6. Further Investigation of the Differentiability Properties of Generalized Solutions; CHAPTER 6. QUASILINEAR EQUATIONS OF THE GENERAL FORM; 1. A Bound for the Norm |u|l,a in Terms of the Norm|u|l,0; 2. A Bound for max |?u|; 3. Existence Theorems; 4. Two-Dimensional Problems; CHAPTER 7. LINEAR SYSTEMS OF ELLIPTIC EQUATIONS; 1. Generalized Solutions in W12 (O); 2. A Bound for max O |u|
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3. A Bound for |u|a,O
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English
Additional Edition:
ISBN 0-12-432850-4
Language:
English
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