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edited Jun 27, 2022 at 10:34

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sobolev-spaces duality lebesgue-measure

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asked Jun 27, 2022 at 10:19

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$f=0$ in $H^{-1}(\Omega)$ implies $f=0$ almost everywhere

Does $f=0$ in $H^{-1}(\Omega)=(H^1_0(\Omega))^*$ implies $f=0$ almost everywhere in $\Omega$?

sobolev-spaces duality