In this paper we show that the solutions of a divergence form elliptic equation with piece-wise Hoelder continuous coefficients have optimal regularity. The problem arises in studying afiber-reinforced composite media described as a domain D with a finite number of subdomains representing the fibers. The coefficients of the operator loose regularity along the boundaries of the subdomains. We prove that the solution is of class C^{1, alpha}.
A sharp regularity result of solutions of a transmission problem / Citti G.;Ferrari F.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 140:(2012), pp. 615-620. [10.1090/S0002-9939-2011-10916-X]
A sharp regularity result of solutions of a transmission problem
CITTI, GIOVANNA;FERRARI, FAUSTO
2012
Abstract
In this paper we show that the solutions of a divergence form elliptic equation with piece-wise Hoelder continuous coefficients have optimal regularity. The problem arises in studying afiber-reinforced composite media described as a domain D with a finite number of subdomains representing the fibers. The coefficients of the operator loose regularity along the boundaries of the subdomains. We prove that the solution is of class C^{1, alpha}.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
