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WEIGHTED ESTIMATES ON FRACTAL DOMAINS

Part of: Classical measure theory Elliptic equations and systems

Published online by Cambridge University Press:  03 February 2015

Raffaela Capitanelli  and
Maria Agostina Vivaldi
Raffaela Capitanelli
Affiliation:
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, “Sapienza Università di Roma”, Via A. Scarpa 16, 00161 Roma, Italy email raffaela.capitanelli@uniroma1.it
Maria Agostina Vivaldi
Affiliation:
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, “Sapienza Università di Roma”, Via A. Scarpa 16, 00161 Roma, Italy email maria.vivaldi@sbai.uniroma1.it
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Abstract

The aim of the paper is to establish estimates in weighted Sobolev spaces for the solutions of the Dirichlet problems on snowflake domains, as well as uniform estimates for the solutions of the Dirichlet problems on pre-fractal approximating domains.

MSC classification

Primary: 28A80: Fractals 35J08: Green's functions 35J25: Boundary value problems for second-order elliptic equations

Information

Type
Research Article
Information
Mathematika , Volume 61 , Issue 2 , May 2015 , pp. 370 - 384
Copyright
Copyright © University College London 2015 

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