Well-posedness of the first order of accuracy difference scheme for elliptic-parabolic equations in Hölder spaces (Q696021)

Summary: A first order of accuracy difference scheme for the approximate solution of abstract nonlocal boundary value problem \(-d^2 u(t)/dt^2 + \text{sign}(t)Au(t) = g(t), (0 \leq t \leq 1), du(t)/dt + \text{sign}(t)Au(t) = f(t), (-1 \leq t \leq 0), u(0+) = u(0-), u'(0-)\) and \(u(1) = u(-1) + \mu\) 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.