Positivity of TwoDimensional Elliptic Differential Operators with Nonlocal Conditions
Abstract
In the present paper, the differential operator A defined by Au = u_{tt}(t,x)u_{xx}(t,x)+ u(t,x) with domain D(A) = {u(t,x):u_{tt},u_{xx},u∈C([0,1]×R),u(0,x) = u(1,x),ut(0,x) = ut(1,x),t∈[0, 1],x∈R} is considered. The Green function for A is constructed. The estimates for the Green function are obtained and the positivity of A in the Banach space C([0,1]×R) is established. The structure of fractional spaces generated by A is investigated, the equivalence of the norm of these fractional spaces and Hölder spaces is established. The positivity of A in the Hölder space C^{2β}([0,1]×R), 0<β<1/2 is obtained.
 Publication:

Numerical Analysis and Applied Mathematics ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics
 Pub Date:
 September 2011
 DOI:
 10.1063/1.3636803
 Bibcode:
 2011AIPC.1389..605A
 Keywords:

 mathematical operators;
 partial differential equations;
 boundaryvalue problems;
 problem solving;
 02.30.Tb;
 02.30.Jr;
 02.60.Lj;
 02.60.Cb;
 Operator theory;
 Partial differential equations;
 Ordinary and partial differential equations;
 boundary value problems;
 Numerical simulation;
 solution of equations