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...

Descripción completa

Guardado en:
Detalles Bibliográficos
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
Descripción
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.

Ejemplares similares