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Corrected a few typos.
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Jochen Glueck
Jochen Glueck
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Let $$V = \left\{ {v \in {H^2}(0,1):{v_x}\left( 0 \right) - v\left( 0 \right) = {v_x}\left( 1 \right) + v\left( 1 \right) = 0} \right\}.$$

Question: Is $V$ dense in ${H^1}\left( {0,1} \right)$?

I know ${C^\infty }\left( \mathbb{R} \right)$ is dense in ${H^1}\left( {0,1} \right)$. But i cantI can't prove that $V$ is dense in ${H^1}\left( {0,1} \right)$ .

Let $$V = \left\{ {v \in {H^2}(0,1):{v_x}\left( 0 \right) - v\left( 0 \right) = {v_x}\left( 1 \right) + v\left( 1 \right) = 0} \right\}.$$

Question: Is $V$ dense in ${H^1}\left( {0,1} \right)$?

I know ${C^\infty }\left( \mathbb{R} \right)$ dense in ${H^1}\left( {0,1} \right)$. But i cant prove that $V$ is dense in ${H^1}\left( {0,1} \right)$ .

Let $$V = \left\{ {v \in {H^2}(0,1):{v_x}\left( 0 \right) - v\left( 0 \right) = {v_x}\left( 1 \right) + v\left( 1 \right) = 0} \right\}.$$

Question: Is $V$ dense in ${H^1}\left( {0,1} \right)$?

I know ${C^\infty }\left( \mathbb{R} \right)$ is dense in ${H^1}\left( {0,1} \right)$. But I can't prove that $V$ is dense in ${H^1}\left( {0,1} \right)$ .

Removed imperative mood and added PDE tag.
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Jochen Glueck
Jochen Glueck
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Let $$V = \left\{ {v \in {H^2}:{v_x}\left( 0 \right) - v\left( 0 \right) = {v_x}\left( 1 \right) + v\left( 1 \right) = 0} \right\}.$$ Prove or disprove that$$V = \left\{ {v \in {H^2}(0,1):{v_x}\left( 0 \right) - v\left( 0 \right) = {v_x}\left( 1 \right) + v\left( 1 \right) = 0} \right\}.$$

Question: Is $V$ is dense in ${H^1}\left( {0,1} \right)$.?

I know ${C^\infty }\left( \mathbb{R} \right)$ dense in ${H^1}\left( {0,1} \right)$. But i cant prove that $V$ is dense in ${H^1}\left( {0,1} \right)$ .

Let $$V = \left\{ {v \in {H^2}:{v_x}\left( 0 \right) - v\left( 0 \right) = {v_x}\left( 1 \right) + v\left( 1 \right) = 0} \right\}.$$ Prove or disprove that $V$ is dense in ${H^1}\left( {0,1} \right)$. I know ${C^\infty }\left( \mathbb{R} \right)$ dense in ${H^1}\left( {0,1} \right)$. But i cant prove that $V$ is dense in ${H^1}\left( {0,1} \right)$ .

Let $$V = \left\{ {v \in {H^2}(0,1):{v_x}\left( 0 \right) - v\left( 0 \right) = {v_x}\left( 1 \right) + v\left( 1 \right) = 0} \right\}.$$

Question: Is $V$ dense in ${H^1}\left( {0,1} \right)$?

I know ${C^\infty }\left( \mathbb{R} \right)$ dense in ${H^1}\left( {0,1} \right)$. But i cant prove that $V$ is dense in ${H^1}\left( {0,1} \right)$ .

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Trần Quang Minh
Trần Quang Minh
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Dense set in Sobolev space ${H^1}\left( {0,1} \right)$

Let $$V = \left\{ {v \in {H^2}:{v_x}\left( 0 \right) - v\left( 0 \right) = {v_x}\left( 1 \right) + v\left( 1 \right) = 0} \right\}.$$ Prove or disprove that $V$ is dense in ${H^1}\left( {0,1} \right)$. I know ${C^\infty }\left( \mathbb{R} \right)$ dense in ${H^1}\left( {0,1} \right)$. But i cant prove that $V$ is dense in ${H^1}\left( {0,1} \right)$ .