Uniform weighted estimates on pre-fractal domains

Raffaela Capitanelli; Maria Agostina Vivaldi

doi:10.3934/dcdsb.2014.19.1969

Article Contents

2014, Volume 19, Issue 7: 1969-1985. Doi: 10.3934/dcdsb.2014.19.1969

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Uniform weighted estimates on pre-fractal domains

Raffaela Capitanelli^1, and
Maria Agostina Vivaldi^1,

1.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Università di Roma "Sapienza", Via A. Scarpa 16, 00161 Roma

Received: April 2013

Revised: January 2014

Published: September 2014

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Abstract

We establish uniform estimates in weighted Sobolev spaces for the solutions of the Dirichlet problems on snowflake pre-fractal domains.

Keywords:

Fractals,
boundary value problems for second-order elliptic equations,
regularity.

Mathematics Subject Classification: Primary: 28A80; Secondary: 35J25, 35D35.

Citation:

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