In this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as p → ∞ {p oinfty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in ω or for data f (that do not change sign in ω) possibly vanishing in a set of positive measure.
Limit of p-Laplacian obstacle problems / Capitanelli, R.; Vivaldi, M. A.. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - 15:2(2022), pp. 265-286. [10.1515/acv-2019-0058]
Limit of p-Laplacian obstacle problems
Capitanelli R.
;Vivaldi M. A.
2022
Abstract
In this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as p → ∞ {p oinfty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in ω or for data f (that do not change sign in ω) possibly vanishing in a set of positive measure.File | Dimensione | Formato | |
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