Examinando por Autor "Buccheri, Stefano"
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Publicación The best approximation of a given function in L2-norm by Lipschitz functions with gradient constraint(De Gruyter, 2024-04-24) Buccheri, Stefano; Leonori, Tommaso; Rossi, Julio D.; https://orcid.org/0000-0002-0667-233X; https://orcid.org/0000-0002-0848-4463; https://orcid.org/0000-0002-5905-4412Publicación Large solutions to quasilinear problems involving the p-Laplacian as p diverges(Springer Nature, 2021-01-18) Buccheri, Stefano; Leonori, TommasoPublicación Strong convergence of the gradients for p-Laplacian problems as p → ∞(Elsevier, 2021-03-01) Buccheri, Stefano; Leonori, Tommaso; Rossi, Julio D.In this paper we prove that the gradients of solutions to the Dirichlet problem for −∆pup = f , with f > 0, converge as p → ∞ strongly in every Lq with 1 ≤ q < ∞ to the gradient of the limit function. This convergence is sharp since a simple example in 1-d shows that there is no convergence in L∞. For a nonnegative f we obtain the same strong convergence inside the support of f . The same kind of result also holds true for the eigenvalue problem for a suitable class of domains (as balls or stadiums).