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Elliptic Functional Differential Equations and Applications Book

Elliptic Functional Differential Equations and Applications
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Elliptic Functional Differential Equations and Applications, Boundary value problems for elliptic differential-difference equations have some astonishing properties. For example, unlike elliptic differential equations, the smoothness of the generalized solutions can be broken in a bounded domain and is preserved on, Elliptic Functional Differential Equations and Applications
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  • Elliptic Functional Differential Equations and Applications
  • Written by author Alexander L. Skubachevskii
  • Published by Birkhauser Basel, 7/31/2012
  • Boundary value problems for elliptic differential-difference equations have some astonishing properties. For example, unlike elliptic differential equations, the smoothness of the generalized solutions can be broken in a bounded domain and is preserved on
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Authors

Acknowledgments
Notation
Introduction 1
1 Ordinary Differential Equations with Nonlocal Boundary Conditions 19
2 Difference Operators in One Dimension 26
3 The Boundary Value Problem for the Differential-Difference Equation 37
4 Generalized and Classical Solutions 53
5 Applications to Control Systems with Delay 71
6 The Boundary Value Problem for the Differential-Difference Equation with Degeneration 77
7 Some Geometrical Constructions 92
8 Difference Operators in the Multidimensional Case 96
9 Necessary and Sufficient Conditions for Strong Ellipticity 109
10 Solvability and Spectrum 122
11 Smoothness of Generalized Solutions in Subdomains 125
12 Smoothness of Solutions on a Boundary of Neighboring Subdomains 138
13 Elliptic Differential Equations with Nonlocal Conditions on Shifts of Boundary 147
14 The Elastic Model 161
15 Variational and Boundary Value Problems 166
16 Smoothness of Solutions 177
17 The One-Dimensional Case 180
18 Self-Adjoint Extension of a Semi-Bounded Differential-Difference Operator 187
19 The Spectrum of Semi-Bounded Differential-Difference Operators 193
20 Smoothness of Solutions of Equations with Degeneration 198
21 Nonlocal Elliptic Problems with a Parameter 211
22 Elliptic Equations with Nonlocal Boundary Conditions in a Cylinder 218
23 Elliptic Differential-Difference Equations in a Cylinder 225
24 Applications to the Multidimensional Diffusion Processes 230
25 Elliptic Problems with Nonlocal Conditions near the Boundary and Feller Semigroups 240
App. A Linear Operators 249
App. B Functional spaces 256
App. C Elliptic Problems 267
Bibliography 275
List of Symbols 285
Index 292


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Elliptic Functional Differential Equations and Applications, Boundary value problems for elliptic differential-difference equations have some astonishing properties. For example, unlike elliptic differential equations, the smoothness of the generalized solutions can be broken in a bounded domain and is preserved on, Elliptic Functional Differential Equations and Applications

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Elliptic Functional Differential Equations and Applications, Boundary value problems for elliptic differential-difference equations have some astonishing properties. For example, unlike elliptic differential equations, the smoothness of the generalized solutions can be broken in a bounded domain and is preserved on, Elliptic Functional Differential Equations and Applications

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Elliptic Functional Differential Equations and Applications, Boundary value problems for elliptic differential-difference equations have some astonishing properties. For example, unlike elliptic differential equations, the smoothness of the generalized solutions can be broken in a bounded domain and is preserved on, Elliptic Functional Differential Equations and Applications

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