= Solution
If an admissible $u$ attained the <infimum> zero, each nonnegative term of its integrand would vanish <almost everywhere>. In particular $|u|^{2011}=0$ <almost everywhere>, so $u=0$ in its <Sobolev space> and its <weak derivative> is zero. But then the remaining term is $(-64)^2=4096$ <almost everywhere>, giving $I(u)=4096$, a contradiction. Thus \b[the <infimum> is zero but no global minimizer exists]. The oscillatory sequence has no convergence of derivatives compatible with substitution into this nonconvex energy.
Back to article page
