NONLINEAR MEAN-VALUE FORMULAS on FRACTAL SETS
In this paper we study the solutions to nonlinear mean-value formulas on fractal sets. We focus on the mean-value problem 1 2maxq Vm,p{f(q)} + 1 2minq Vm,p{f(q)}-f(p) = 0 in the Sierpiński gasket with prescribed values f(p1), f(p2) and f(p3) at the three vertices of the first triangle. For this prob...
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2018
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0218348X_v26_n6_p_Navarro http://hdl.handle.net/20.500.12110/paper_0218348X_v26_n6_p_Navarro |
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| Sumario: | In this paper we study the solutions to nonlinear mean-value formulas on fractal sets. We focus on the mean-value problem 1 2maxq Vm,p{f(q)} + 1 2minq Vm,p{f(q)}-f(p) = 0 in the Sierpiński gasket with prescribed values f(p1), f(p2) and f(p3) at the three vertices of the first triangle. For this problem we show existence and uniqueness of a continuous solution and analyze some properties like the validity of a comparison principle, Lipschitz continuity of solutions (regularity) and continuous dependence of the solution with respect to the prescribed values at the three vertices of the first triangle. © 2018 World Scientific Publishing Company. |
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