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\title{HW 4 for Calculus of Variations 2012}
\author{Andrej Cherkaev}

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\maketitle

1. Compute convex envelopes of the functions
$$
f_1(u)= \min\left\{ (u-1)^2, (u+1)^2 \right\} 
$$

$$
f_1(u_1, u_2)= \left\{ \begin{array}{ll}
 0 & \mbox{ if } u_1^2 + u_2^2=0 \\
1+ u_1^2 + u_2^2 & ~~~\mbox{ otherwise }
\end{array}
\right 
$$

$$
f_3(u)= \sqrt{|u|}
$$

Consider variational problems 
$$
\inf 
$$


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