Limit of \(p\)-Laplacian obstacle problems. (English) Zbl 1486.35233
Summary: In this paper, we study asymptotic behavior of solutions to obstacle problems for \(p\)-Laplacians as \(p\to\infty\). 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 \(\Omega\) or for data \(f\) (that do not change sign in \(\Omega)\) possibly vanishing in a set of positive measure.
MSC:
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35B40 | Asymptotic behavior of solutions to PDEs |
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