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Inverse problem

Regularization of an inverse problem

Variational regularization

Total variation seminorm on a domain

Function of bounded variation on a domain

Zero-mean bounded-variation space

{c}

On a bounded Lipschitz domain,
$$
\|u-u_\Omega\|_{L^1(\Omega)}\leq C_\Omega\operatorname{TV}(u),
\qquad
u_\Omega=|\Omega|^{-1}\int_\Omega u.
$$
It reduces to $\|u\|_{L^1}\leq C_\Omega\operatorname{TV}(u)$ on $BV_0(\Omega)$.


Poincaré inequality for total variation

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 326 / 2 / 1 / Solution

Poincaré inequality for total variation

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Poincaré inequality for total variation

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