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{\bf Necessary Conditions for Weak Lower Semicontinuity on\\
Domains with Infinite Measure}

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Stefan Kr\"omer\\
Department of Mathematical Sciences\\
Carnegie Mellon University\\
Pittsburgh, PA  15213\\
kroemers@andrew.cmu.edu 
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\noindent {\bf Abstract}:  We derive sharp necessary conditions for weak
sequential lower semicontinuity of integral functionals on Sobolev spaces, with
an integrand which only depends on the gradient of a scalar field over a
domain in $\mathbb{R}^n$.  An emphasis is put on domains with infinite
measure, and the integrand is allowed to assume the value $+ \infty$.

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