Pseudodifferential Operators and Elliptic Regularity
نویسنده
چکیده
Theorem 1. Let M be a compact manifold, E and F be two (smooth) vector bundles over M , and P : C∞(M ;E) → C∞(M ;F ) be a differential operator (with smooth coefficients) of order n. Assume that P is elliptic, in the sense defined in the next section. Then: 1. The operator P (or rather its relevant extension) is Fredholm W n 2 (M ;E)→ L(M ;F ). Here W n 2 is a Sobolev space (introduced below). (The question of the index of P is extremely interesting, but falls outside of this talk.)
منابع مشابه
Pseudodifferential Operators And Nonlinear PDE
CONTENTS Introduction. 0. Pseudodifferential operators and linear PDE. §0.1 The Fourier integral representation and symbol classes §0.2 Schwartz kernels of pseudodifferential operators §0.3 Adjoints and products §0.4 Elliptic operators and parametrices §0.5 L 2 estimates §0.6 Gårding's inequality §0.7 The sharp Gårding inequality §0.8 Hyperbolic evolution equations §0.9 Egorov's theorem §0.10 M...
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