In this paper we study the asymptotic behavior of the functional $$ F_\epsilon(u) := \int_\Omega \epsilon |\nabla u|^2 + \epsilon^{-3} \beta(u/\eps) dx $$ where $\beta$ is a non-negative lower semicontinuous function with compact support. When $\epsilon$ tends to $0$, the limit functional corresponds to a least area problem with an obstacle.
Singular perturbation problems with a compact support semilinear term
ALBERTI, GIOVANNI;BUTTAZZO, GIUSEPPE
1994-01-01
Abstract
In this paper we study the asymptotic behavior of the functional $$ F_\epsilon(u) := \int_\Omega \epsilon |\nabla u|^2 + \epsilon^{-3} \beta(u/\eps) dx $$ where $\beta$ is a non-negative lower semicontinuous function with compact support. When $\epsilon$ tends to $0$, the limit functional corresponds to a least area problem with an obstacle.File in questo prodotto:
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