Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces

A first order of accuracy difference scheme for theapproximate solution of abstract nonlocal boundary value problem −2()/2+sign()()=(), (0≤≤1), ()/+sign()()=(), (−1≤≤0), (0+)=(0−),(0+)=(0−),and(1)=(−1)+ for differential equations in a Hilbert space with a self-adjoint positive definite operator A is considered. The well-posedness of this difference scheme in Hölder spaces without a weight is established. Moreover, as applications, coercivity estimates in Hölder normsfor the solutions of nonlocal boundary value problems for elliptic-parabolic equations are obtained