The structure of fractional spaces generated by a two-dimensional elliptic differential operator and its applications
1 Department of Mathematics, Fatih University, 34500, Buyukcekmece, Istanbul, Turkey
2 Department of Mathematics, ITTU, Ashgabat, Turkmenistan
3 Present address: Fen Fakultesi, Matematik Bolumu, Hacettepe Universitesi, 06800, Beytepe, Ankara, Turkey
Boundary Value Problems 2014, 2014:3 doi:10.1186/1687-2770-2014-3Published: 2 January 2014
We consider the two-dimensional differential operator defined on functions on the half-plane with the boundary conditions , , where , , are continuously differentiable and satisfy the uniform ellipticity condition , . The structure of the fractional spaces generated by the operator A is investigated. The positivity of A in Hölder spaces is established. In applications, theorems on well-posedness in a Hölder space of elliptic problems are obtained.
MSC: 35J25, 47E05, 34B27.