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We show that for arbitrary nonlinearities $f$ and $g$ that the extremal solutions associated with $ (G)_{\\lambda,\\gamma}$ are bounded provided $ \\Omega$ is a convex domain in $ \\mathbb R^N$ where $ N \\le 3$. 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We show that for arbitrary nonlinearities $f$ and $g$ that the extremal solutions associated with $ (G)_{\\lambda,\\gamma}$ are bounded provided $ \\Omega$ is a convex domain in $ \\mathbb R^N$ where $ N \\le 3$. 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