Uniform weighted estimates on pre-fractal domains
Raffaela Capitanelli Maria Agostina Vivaldi
Discrete & Continuous Dynamical Systems - B 2014, 19(7): 1969-1985 doi: 10.3934/dcdsb.2014.19.1969
We establish uniform estimates in weighted Sobolev spaces for the solutions of the Dirichlet problems on snowflake pre-fractal domains.
keywords: boundary value problems for second-order elliptic equations regularity. Fractals
Robin boundary condition on scale irregular fractals
Raffaela Capitanelli
Communications on Pure & Applied Analysis 2010, 9(5): 1221-1234 doi: 10.3934/cpaa.2010.9.1221
We consider mixed Dirichlet-Robin problems on scale irregular domains. In particular, we study the asymptotic convergence of the solutions of elliptic problems with Robin boundary conditions on the "prefractal" curves approximating the scale irregular fractals.
keywords: irregular interfaces. fractals Mixed Dirichlet-Robin problems
Asymptotics for quasilinear obstacle problems in bad domains
Raffaela Capitanelli Salvatore Fragapane
Discrete & Continuous Dynamical Systems - S 2019, 12(1): 43-56 doi: 10.3934/dcdss.2019003

We study two obstacle problems involving the p-Laplace operator in domains with n-th pre-fractal and fractal boundary. We perform asymptotic analysis for $p \to \infty $ and $n \to \infty $.

keywords: Fractals degenerate elliptic equations variational methods for second-order elliptic equations quasilinear elliptic equations with p-Laplacian asymptotic behavior of solutions
Raffaela Capitanelli Maria Rosaria Lancia Maria Agostina Vivaldi
Discrete & Continuous Dynamical Systems - S 2019, 12(1): ⅰ-ⅰ doi: 10.3934/dcdss.201901i

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