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2021-03-01
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info:eu-repo/semantics/openAccess
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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).
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Stefano Buccheri, Tommaso Leonori, Julio D. Rossi, Strong convergence of the gradients for p-Laplacian problems as p → ∞, Journal of Mathematical Analysis and Applications, Volume 495, Issue 1, 2021, 124724, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2020.124724.
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Facultad de Ciencias
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Matemáticas Fundamentales