 Solution

ID: past-exam-of-the-calculus-of-variations-course-of-the-university-of-oxford/2010/1/a/i/solution

\overset{u}{ˉ}

for which there is

ρ > 0

such that

I (v) \geq I (\overset{u}{ˉ}) whenever v \in A, ∥ v - \overset{u}{ˉ} ∥_{W^{1, \infty}} < ρ .

The Sobolev norm controls both the function and its first weak derivative. The boundary values remain fixed because both functions are admissible.

 New to topics? Read the docs here!