K. Biroud - Academia.edu (original) (raw)
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Università degli Studi di Milano - State University of Milan (Italy)
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Papers by K. Biroud
Communications in Contemporary Mathematics, 2015
Let Ω ⊂ ℝN be a bounded regular domain of ℝN and 1 < p < ∞. The paper is divided into two m... more Let Ω ⊂ ℝN be a bounded regular domain of ℝN and 1 < p < ∞. The paper is divided into two main parts. In the first part, we prove the following improved Hardy inequality for convex domains. Namely, for all [Formula: see text], we have [Formula: see text] where d(x) = dist (x, ∂Ω), [Formula: see text] and C is a positive constant depending only on p, N and Ω. The optimality of the exponent of the logarithmic term is also proved. In the second part, we consider the following class of elliptic problem [Formula: see text] where 0 < q ≤ 2* - 1. We investigate the question of existence and nonexistence of positive solutions depending on the range of the exponent q.
Complex Variables and Elliptic Equations, Jun 26, 2018
Journal of Evolution Equations, 2015
Communications in Contemporary Mathematics, 2015
Let Ω ⊂ ℝN be a bounded regular domain of ℝN and 1 < p < ∞. The paper is divided into two m... more Let Ω ⊂ ℝN be a bounded regular domain of ℝN and 1 < p < ∞. The paper is divided into two main parts. In the first part, we prove the following improved Hardy inequality for convex domains. Namely, for all [Formula: see text], we have [Formula: see text] where d(x) = dist (x, ∂Ω), [Formula: see text] and C is a positive constant depending only on p, N and Ω. The optimality of the exponent of the logarithmic term is also proved. In the second part, we consider the following class of elliptic problem [Formula: see text] where 0 < q ≤ 2* - 1. We investigate the question of existence and nonexistence of positive solutions depending on the range of the exponent q.
Complex Variables and Elliptic Equations, Jun 26, 2018
Journal of Evolution Equations, 2015