Open AccessAsymptotics for Venttsel' problems for operators in non divergence form in irregular domains
Author(s) -
Maria Rosaria Lancia,
Valerio Regis Durante,
Paola Vernole
Publication year - 2016
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2016060
Subject(s) - mathematics , uniqueness , divergence (linguistics) , semigroup , fractal , domain (mathematical analysis) , limit (mathematics) , operator (biology) , pure mathematics , mathematical analysis , linguistics , philosophy , biochemistry , chemistry , repressor , transcription factor , gene
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