| Abstract: |
| In this talk we study obstacle problems for the regional fractional $p$-Laplacian in a domain $\Omega\subset\mathbb{R}^2$ having fractal boundary of Koch type. We first prove well-posedness results for the solution of the obstacle problem, as well as two equivalent formulations. Then, we study corresponding approximating obstacle problems in a sequence of domains $\Omega_n\subset\mathbb{R}^2$ having pre-fractal boundary, for $n\in\mathbb{N}$. After proving the well-posedness of the approximating obstacle problems, we perform the asymptotic analysis for both $n\to+\infty$ and $p\to+\infty$. |
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