Optimal Estimates for the Conductivity Problem by Green’s Function Method
| Autor: | Hongjie Dong, Haigang Li |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Class (set theory)
Mechanical Engineering Open problem 010102 general mathematics Isotropy Complex system Derivative Conductivity 01 natural sciences 010101 applied mathematics symbols.namesake Mathematics (miscellaneous) Green's function symbols Applied mathematics 0101 mathematics Divergence (statistics) Analysis Mathematics |
| Zdroj: | Archive for Rational Mechanics and Analysis. 231:1427-1453 |
| ISSN: | 1432-0673 0003-9527 |
| Popis: | We study a class of second-order elliptic equations of divergence form, with discontinuous coefficients and data, which models the conductivity problem in composite materials. We establish optimal gradient estimates by showing the explicit dependence of the elliptic coefficients and the distance between interfacial boundaries of inclusions. These extend the known results in the literature and answer open problem (b) proposed by Li and Vogelius (2000) for the isotropic conductivity problem. We also obtain more interesting higher-order derivative estimates, which answers open problem (c) of Li and Vogelius (2000). It is worth pointing out that the equations under consideration in this paper are non-homogeneous. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink