Asymptotics for Venttsel' problems for operators in non divergence form in irregular domains

Maria Rosaria  Lancia; Valerio Regis  Durante; Paola  Vernole

doi:10.3934/dcdss.2016060

Article Contents

2016, Volume 9, Issue 5: 1493-1520. Doi: 10.3934/dcdss.2016060

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Asymptotics for Venttsel' problems for operators in non divergence form in irregular domains

1.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza, Università di Roma, Via A. Scarpa 16, 00161 Roma
2.
Università degli studi Roma 3, Dipartimento di Matematica, Largo San Leonardo Murialdo 1, 00146 Roma
3.
Dipartimento di Matematica, Universita degli Studi di Roma "La Sapienza", P.zale Aldo Moro 2, 00185 Roma

Received: November 30, 2014

Revised: June 30, 2015

Published: September 2016

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Abstract

We study a Venttsel' problem in a three dimensional fractal domain for an operator in non divergence form. We prove existence, uniqueness and regularity results of the strict solution for both the fractal and prefractal problem, via a semigroup approach. In view of numerical approximations, we study the asymptotic behaviour of the solutions of the prefractal problems and we prove that the prefractal solutions converge in the Mosco-Kuwae-Shioya sense to the (limit) solution of the fractal one.

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Mathematics Subject Classification: Primary: 35K, 28A80; Secondary: 31C25, 47D06.

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