We prove existence and uniqueness of the weak solution for a second order semilinear transmission problem in a bounded domain in R-3 in the case of a Koch-type fractal layer S or the corresponding prefractal layer approximating S. We study the asymptotic behavior of the solutions of the corresponding prefractal problem and we prove regularity results for the weak solution via a generalized Green formula for domains with fractal boundaries. (C) 2012 Elsevier Ltd. All rights reserved.
Semilinear fractal problems: Approximation and regularity results / Lancia, Maria Rosaria; Vernole, Paola. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - ELETTRONICO. - 80:(2013), pp. 216-232. [10.1016/j.na.2012.08.020]
Semilinear fractal problems: Approximation and regularity results
LANCIA, Maria Rosaria;VERNOLE, Paola
2013
Abstract
We prove existence and uniqueness of the weak solution for a second order semilinear transmission problem in a bounded domain in R-3 in the case of a Koch-type fractal layer S or the corresponding prefractal layer approximating S. We study the asymptotic behavior of the solutions of the corresponding prefractal problem and we prove regularity results for the weak solution via a generalized Green formula for domains with fractal boundaries. (C) 2012 Elsevier Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
