Semilinear equations with exponential nonlinearity and measure data

Daniele Bartolucci; Fabiana Leoni; Luigi Orsina; Augusto C. Ponce

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Necessary conditions for weak lower semicontinuity on domains with infinite measure

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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 $+ \infty$ .