Degenerate Elliptic Equations

✍ Scribed by Serge Levendorskii (auth.)

• Publisher: Springer Netherlands
• Year: 1993
• Tongue: English
• Leaves: 442
• Series: Mathematics and Its Applications 258
• Edition: 1
• Category: Library

✦ Synopsis

This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Gårding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed.
For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.

✦ Table of Contents

Front Matter....Pages i-xi
Introduction....Pages 1-8
General Calculus of Pseudodifferential Operators....Pages 9-73
Model Classes of Degenerate Elliptic Differential Operators....Pages 75-127
General Classes of Degenerate Elliptic Differential Operators....Pages 129-162
Degenerate Elliptic Operators in Non — Power — Like Degeneration Case....Pages 163-170
L p — Theory for Degenerate Elliptic Operators....Pages 171-185
Coersiveness of Degenerate Quadratic Forms....Pages 187-202
Some Classes of Hypoelliptic Pseudodifferential Operators on Closed Manifold....Pages 203-244
Algebra of Boundary Value Problems for Class of Pseudodifferential Operators which Change Order on the Boundary....Pages 245-278
General Schemes of Investigation of Spectral Asymptotics for Degenerate Elliptic Equations....Pages 279-300
Spectral Asymptotics of Degenerate Elliptic Operators....Pages 301-334
Spectral Asymptotics of Hypoelliptic Operators with Multiple Characteristics....Pages 335-387
Back Matter....Pages 389-436

✦ Subjects

Partial Differential Equations;Vibration, Dynamical Systems, Control;Quantum Physics;Integral Transforms, Operational Calculus;Integral Equations