Nonlinear Mean-Value Formulas on Fractal Sets

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Title: Nonlinear Mean-Value Formulas on Fractal Sets
Authors: Navarro Climent, José Carlos | Rossi, Julio D.
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Mean-Value Formulas | Fractal Sets
Knowledge Area: Análisis Matemático
Issue Date: 24-Dec-2018
Publisher: World Scientific Publishing
Citation: Fractals. 2018, 26(6): 1850091. doi:10.1142/S0218348X18500913
Abstract: In this paper we study the solutions to nonlinear mean-value formulas on fractal sets. We focus on the mean-value problem 12maxq∈Vm,p{f(q)}+12minq∈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.
Sponsor: Supported by MEC MTM2010-18128 and MTM2011-27998 (Spain).
ISSN: 0218-348X (Print) | 1793-6543 (Online)
DOI: 10.1142/S0218348X18500913
Language: eng
Type: info:eu-repo/semantics/article
Rights: © 2018 World Scientific Publishing
Peer Review: si
Publisher version:
Appears in Collections:INV - CADAGL - Artículos de Revistas

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