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Decay estimates for solutions to non-autonomous critical p-Laplace problems
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We prove optimal decay estimates for positive solutions to elliptic p-Laplacian problems in the entire Euclidean space, when a critical nonlinearity with a decaying source term is considered. Also gradient decay estimates are furnished. Our results extend previous theorems in the literature, in which a purely critical reaction is treated. The technique is based on a priori estimates, regularity results, and rescaling arguments, combined with the doubling lemma.
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Existence and decay for a Grushin problem in $\mathbb{R}^N$ with singular, convective, critical reaction
A positive weak solution exists for a Grushin problem in the whole space mixing singular, convective, and critical reactions, with decay at infinity in the non-convective case.
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