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Elliptic, parabolic and hyperbolic operators. Laplace, Laplace-Beltrami, Schrödinger, Dirac. Exterior derivative and Lie derivative operators.

1 vote
0 answers
229 views

Fredholmness of elliptic operator on Hölder spaces

Let $(M,g)$ be a smooth oriented closed Riemannian manifold, $E\to M$ a smooth vector bundle, and $C^{k,\alpha}(E)$ the Banach space of sections of $E$ that are $k$-times differentiable (with respect …
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2 votes
0 answers
62 views

Singularity of reproducing kernel for elliptic operator

Let $(M,g)$ be a smooth compact Riemannian manifold and dimension $2$, $\Gamma$ a smooth vector bundle over $M$, and suppose $L: W^{k,2}(\Gamma)\to W^{k-2,2}(\Gamma)$ is a second order strongly ellipt …
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