Foundations of the Classical Theory of Partial Differential EquationsSpringer Science & Business Media, 1 déc. 2013 - 259 pages From the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery...." The Mathematical Gazette, 1993 |
Table des matières
| 6 | |
4 Hyperbolic Equations | 14 |
2 The CauchyKovalevskaya Theorem and Its Generalizations | 28 |
3 Classification of Linear Differential Equations Reduction | 37 |
8 | 39 |
The Classical Theory | 47 |
Linear Differential Operators in Spaces of Distributions | 58 |
2 Elliptic Equations and BoundaryValue Problems | 82 |
77 | 167 |
7 Exterior BoundaryValue Problems and Scattering Theory | 184 |
8 Spectral Theory of OneDimensional Differential Operators | 199 |
སྐྱེ བ སྐྱ སྐྱ | 206 |
Regular Case | 207 |
9 Special Functions | 220 |
References | 242 |
| 248 | |
81 | 110 |
3 Sobolev Spaces and Generalized Solutions of BoundaryValue | 113 |
5 Parabolic Equations | 163 |
| 250 | |
Autres éditions - Tout afficher
Foundations of the Classical Theory of Partial Differential Equations Yu.V. Egorov,M.A. Shubin Aucun aperçu disponible - 2011 |
Expressions et termes fréquents
analytic arbitrary assume asymptotic boundary conditions boundary-value problem bounded region called Cauchy problem compact set complete orthogonal system consider constant coefficients continuous convergence convolution corresponding defined denote derivatives described differential equations Dirichlet problem distribution ƒ eigenfunctions eigenvalues elliptic equivalent estimate example exists exterior Əxj follows formula Fourier transform function ƒ fundamental solution Green's function H¹(N harmonic function Hilbert holds homogeneous Hörmander hyperbolic operator imbedding infinity initial conditions integral L²(N Laplace's equation Laplacian linear matrix neighborhood Neumann problem norm obtain parabolic particular Petrovskij point xo Poisson's Poisson's equation polynomial potential right-hand side second-order Sect self-adjoint Shilov smooth boundary Sobolev spaces solution of Eq solvable surface symmetric system of eigenfunctions Theorem theory topology unique solution values variables vector vector-valued function verify well-posed zero ди მე