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Para 0 < β < 1 consideramos la ecuación -Δu = χ (-u + λf(x, u)) en Ω con condición de borde tipo Dirichlet. Esta ecuación posee una solución maximal u ≥ 0 para todo λ > 0. Si λ es menor que una cierta constante λ*, u se anula en el interior del dominio creando una frontera libre, y para λ > λ* esta solución es positiva en Ω y estable. Establecemos la regularidad de u incluso en presencia de una frontera libre. Para λ ≥ λ* la solución del problema parabólico singular...
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