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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Detalles Bibliográficos
Publicado: 2018
Materias:
Fractal Sets
Mean-Value Formulas
Geometry
Comparison principle
Continuous dependence
Existence and uniqueness
Fractal sets
Lipschitz continuity
Mean values
Fractals
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
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0218348X_v26_n6_p_Navarro
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spelling paper:paper_0218348X_v26_n6_p_Navarro2023-06-08T15:21:34Z NONLINEAR MEAN-VALUE FORMULAS on FRACTAL SETS Fractal Sets Mean-Value Formulas Geometry Comparison principle Continuous dependence Existence and uniqueness Fractal sets Lipschitz continuity Mean values Fractals 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. 2018 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
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fractal Sets
Mean-Value Formulas
Geometry
Comparison principle
Continuous dependence
Existence and uniqueness
Fractal sets
Lipschitz continuity
Mean values
Fractals
spellingShingle Fractal Sets
Mean-Value Formulas
Geometry
Comparison principle
Continuous dependence
Existence and uniqueness
Fractal sets
Lipschitz continuity
Mean values
Fractals
NONLINEAR MEAN-VALUE FORMULAS on FRACTAL SETS
topic_facet Fractal Sets
Mean-Value Formulas
Geometry
Comparison principle
Continuous dependence
Existence and uniqueness
Fractal sets
Lipschitz continuity
Mean values
Fractals
description 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.
title NONLINEAR MEAN-VALUE FORMULAS on FRACTAL SETS
title_short NONLINEAR MEAN-VALUE FORMULAS on FRACTAL SETS
title_full NONLINEAR MEAN-VALUE FORMULAS on FRACTAL SETS
title_fullStr NONLINEAR MEAN-VALUE FORMULAS on FRACTAL SETS
title_full_unstemmed NONLINEAR MEAN-VALUE FORMULAS on FRACTAL SETS
title_sort nonlinear mean-value formulas on fractal sets
publishDate 2018
url 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
_version_ 1768542735687483392

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