 Solution

ID: past-exam-of-the-partial-differential-equations-for-pure-and-applied-mathematicians-and-calculus-of-variations-course-of-the-university-of-oxford/2008/b/6/a/i/solution

\overset{u}{ˉ}

for which some

ρ > 0

gives

I (v) \geq I (\overset{u}{ˉ})

for all admissible

v

with

∥ v - \overset{u}{ˉ} ∥_{W^{1, \infty}} < ρ

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