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

Abstract EN

A first order of accuracy difference scheme for the approximate solution of abstract nonlocal boundary value problem −d2u(t)/dt2+sign(t)Au(t)=g(t), (0≤t≤1), du(t)/dt+sign(t)Au(t)=f(t), (−1≤t≤0), u(0+)=u(0−),u′(0+)=u′(0−),and u(1)=u(−1)+μ for differential equations in a Hilbert space H 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 norms for the solutions of nonlocal boundary value problems for elliptic-parabolic equations are obtained.