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Can anyone help with this question please? The initial boundary condition is trivial, I struggled to show the first cond...

Can anyone help with this question please? The initial boundary condition is trivial, I struggled to show the first condition.

Any help will be appreciated!!!

Let now Ω c Rd be an open and bounded set with a smooth boundary on and outer unit normal n. Furthermore, let f : Ω → R be a

Let now Ω c Rd be an open and bounded set with a smooth boundary on and outer unit normal n. Furthermore, let f : Ω → R be a continuous function. Define the functional where weg-(u E C10) |v = 0 and ▽u . n = 0 in 201. Show that a minimiser u of I solves
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Crea is an ơpa and bounded car with smooth Criveu tfa. boundary ΌΠ and outer Unit normal ^. Also, f:d2- a 0nSince, ut tu E i) has a uuinjmum at 2ach feIk, tho scalar funehom 0 on *. UuJi

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