On Max–Min Mean Value Formulas on the Sierpinski Gasket
Please use this identifier to cite or link to this item:
http://hdl.handle.net/10045/113744
Title: | On Max–Min Mean Value Formulas on the Sierpinski Gasket |
---|---|
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 | Infinity Harmonic Functions |
Knowledge Area: | Análisis Matemático |
Issue Date: | 4-Feb-2021 |
Publisher: | World Scientific |
Citation: | Fractals. 2021, 29(1): 2150018. https://doi.org/10.1142/S0218348X21500183 |
Abstract: | In this paper, we study solutions to the max–min mean value problem ½ max q∈Vm,p {f(q)} + ½ min q∈Vm,p {f(q)} = f(p) in the Sierpinski Gasket with a prescribed Dirichlet datum at the three vertices of the first triangle. In the previous mean value, formula p is a vertex of one triangle at one stage in the construction of the Sierpinski Gasket and Vm,p is the set of vertices that are adjacent to p at that stage. For this problem, it was known that there are existence and uniqueness of a continuous solution, a comparison principle holds, and, moreover, solutions are Lipschitz continuous. Here we continue the analysis of this problem and prove that the solution is piecewise linear on the segments of the Sierpinski Gasket. Moreover, we also show for which values at the three vertices of the first triangle solutions to this mean value formula coincide with infinity harmonic functions. |
Sponsor: | This study was supported by the CONICET grant PIP GI No. 11220150100036CO (Argentina), UBACyT grant 20020160100155BA (Argentina) and Project MTM2015-70227-P (Spain). |
URI: | http://hdl.handle.net/10045/113744 |
ISSN: | 0218-348X (Print) | 1793-6543 (Online) |
DOI: | 10.1142/S0218348X21500183 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © World Scientific Publishing Company |
Peer Review: | si |
Publisher version: | https://doi.org/10.1142/S0218348X21500183 |
Appears in Collections: | INV - CADAGL - Artículos de Revistas INV - GAM - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Navarro_Rossi_2021_Fractals_final.pdf | Versión final (acceso restringido) | 486,29 kB | Adobe PDF | Open Request a copy |
Items in RUA are protected by copyright, with all rights reserved, unless otherwise indicated.