Abstract
We consider second order uniformly elliptic operators of divergence form in Rd+1 whose coefficients are independent of one variable. Under the Lipschitz condition on the coefficients we characterize the domain of the Poisson operators and the Dirichlet-Neumann maps in the Sobolev space Hs(Rd) for each s∈[0,1]. Moreover, we also show a factorizationformula for the elliptic operator in terms of the Poisson operator.
Original language | English |
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Pages (from-to) | 6227-6252 |
Number of pages | 26 |
Journal | Transactions of the American Mathematical Society |
Volume | 368 |
Issue number | 9 |
DOIs | |
Publication status | Published - 2016 |
Keywords
- DirichletNeumann maps
- Divergence form elliptic operators
- Poisson operators
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics