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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Autores principales: Navarro, J.C., Rossi, J.D.
Formato: JOUR
Materias:
Fractal Sets
Mean-Value Formulas
Geometry
Comparison principle
Continuous dependence
Existence and uniqueness
Fractal sets
Lipschitz continuity
Mean values
Fractals
Acceso en línea: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
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spelling todo:paper_0218348X_v26_n6_p_Navarro2023-10-03T15:11:03Z NONLINEAR MEAN-VALUE FORMULAS on FRACTAL SETS Navarro, J.C. Rossi, J.D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Navarro, J.C.
Rossi, J.D.
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.
format JOUR
author Navarro, J.C.
Rossi, J.D.
author_facet Navarro, J.C.
Rossi, J.D.
author_sort Navarro, J.C.
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
url http://hdl.handle.net/20.500.12110/paper_0218348X_v26_n6_p_Navarro
work_keys_str_mv AT navarrojc nonlinearmeanvalueformulasonfractalsets
AT rossijd nonlinearmeanvalueformulasonfractalsets
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