Necessary Conditions for Weak Lower Semicontinuity on Domains with Infinite Measure

Stefan Krömer Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213 kroemers@andrew.cmu.edu

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 ℝ^{n}. An emphasis is put on domains with infinite measure, and the integrand is allowed to assume the value +∞.