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October 2016, 9(5): 1493-1520. doi: 10.3934/dcdss.2016060
Asymptotics for Venttsel' problems for operators in non divergence form in irregular domains
Maria Rosaria Lancia 1, , Valerio Regis Durante 2, and Paola Vernole 3,
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza, Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy
Università degli studi Roma 3, Dipartimento di Matematica, Largo San Leonardo Murialdo 1, 00146 Roma, Italy
Dipartimento di Matematica, Universita degli Studi di Roma "La Sapienza", P.zale Aldo Moro 2, 00185 Roma, Italy
Received December 2014 Revised July 2015 Published October 2016
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.
Keywords: non divergence form operator, energy forms, semigroups, fractal domains, Asymptotic behaviour, Venttsel' problems, varying Hilbert spaces..
Mathematics Subject Classification: Primary: 35K, 28A80; Secondary: 31C25, 47D0.
Citation: Maria Rosaria Lancia, Valerio Regis Durante, Paola Vernole. Asymptotics for Venttsel' problems for operators in non divergence form in irregular domains. Discrete & Continuous Dynamical Systems - S, 2016, 9 (5) : 1493-1520. doi: 10.3934/dcdss.2016060
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