Author | Taylor, Michael E. author |
---|---|
Title | Pseudodifferential Operators and Nonlinear PDE [electronic resource] / by Michael E. Taylor |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1991 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0431-2 |
Descript | IV, 216 p. online resource |
Introduction. -- 0. Pseudodifferential operators and linear PDE. -- ยง0.1 The Fourier integral representation and symbol classes -- ยง0.2 Schwartz kernels of pseudodifferential operators -- ยง0.3 Adjoints and products -- ยง0.4 Elliptic operators and parametrices -- ยง0.5 L2 estimates -- ยง0.6 Gรฅrdingโs inequality -- ยง0.7 The sharp Gรฅrding inequality -- ยง0.8 Hyperbolic evolution equations -- ยง0.9 Egorovโs theorem -- ยง0.10 Microlocal regularity -- ยง0.11 Lp estimates -- ยง0.12 Operators on manifolds -- 1. Symbols with limited smoothness. -- ยง1.1 Symbol classes -- ยง1.2 Some simple elliptic regularity theorems -- ยง1.3 Symbol smoothing -- 2. Operator estimates and elliptic regularity. -- ยง2.1 Bounds for operators with nonregular symbols -- ยง2.2 Further elliptic regularity theorems -- ยง2.3 Adjoints -- ยง2.4 Sharp Gรฅrding inequality -- 3. Paradifferential operators. -- ยง3.1 Composition and paraproducts -- ยง3.2 Various forms of paraproduct -- ยง3.3 Nonlinear PDE and paradifferential operators -- ยง3.4 Operator algebra -- ยง3.5 Product estimates -- ยง3.6 Commutator estimates -- 4. Calculus for OPC1Sclm. -- ยง4.1 Commutator estimates -- ยง4.2 Operator algebra -- ยง4.3 Gรฅrding inequality -- ยง4.4 C1-paradifferential calculus -- 5. Nonlinear hyperbolic systems. -- ยง5.1 Quasilinear symmetric hyperbolic systems -- ยง5.2 Symmetrizable hyperbolic systems -- ยง5.3 Higher order hyperbolic equations -- ยง5.4 Completely nonlinear hyperbolic systems -- 6. Propagation of singularities. -- ยง6.1 Propagation of singularities -- ยง6.2 Nonlinear formation of singularities -- ยง6.3 Egorovโs theorem -- 7. Nonlinear parabolic systems. -- ยง7.1 Strongly parabolic quasilinear systems -- ยง7.2 Petrowski parabolic quasilinear systems -- ยง7.3 Sharper estimates -- ยง7.4 Semilinear parabolic systems -- 8. Nonlinear elliptic boundary problems. -- ยง8.1 Second order elliptic equations -- ยง8.2 Quasilinear elliptic equations -- ยง8.3 Interface with DeGiorgi-Nash-Moser theory -- 9. Extension of the Schauder estimates. -- ยง9.1 Nirenbergโs refinement -- ยง9.2 Elliptic boundary problems -- A. Function spaces. -- ยงA.1 Hรถlder spaces, Zygmund spaces, and Sobolev spaces -- ยงA.2 Morrey spaces -- ยงA.3 BMO -- B. Sup norm estimates. -- C. DeGiorgi-Nash-Moser estimates. -- ยงC.2 Hรถlder continuity -- ยงC.3 Inhomogeneous equations -- ยงC.4 Boundary regularity -- D. Paraproduct estimates. -- Index of notation. -- References