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

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Definition of spectral gradient

Consider this differential operator $$ \mathcal{H}(\phi(\mathbf{x})) = -\triangle + V(\mathbf{x})H_\epsilon (\phi(\mathbf{x})) $$ where $\mathbf{x} \in \mathbb{R}^2$, $\phi : \mathbb{R}^2 \rightarrow …
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