Show that a function , which minimises, among all smooth functions , s.t. on , solves...

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Question

Show that a function , which minimises,

$\int_{\Omega }^{ }\left | \bigtriangledown v \right |^2dx-2\int_{\Omega }^{ }fvdx$

among all smooth functions , s.t. v = g on $\delta\Omega$ , solves the following equation:

$-\Delta u=f$ in $\Omega$ and u = g on $\delta \Omega$

math Advanced-Math

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Answer 1

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Show that a function , which minimises, among all smooth functions , s.t. on , solves...

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