On the basis of the Morrey type estimate established for linear subelliptic system, we can first prove the (L_{X,mathrm{loc}}^{2,lambda } -regularity for weak solutions of the obstacle problems and then interior Hölder continuity is obtained by virtue of the equivalence between the Campanato space and the Hölder continuity function space (see [34, 35]).
A posteriori error estimates are established for the finite element approximation solutions in Section 3.
Further, optimal error estimates are established for the semi-discrete scheme.
The error estimates are established for two kinds of nonuniform meshes.
Using Rademacher type, maximal estimates are established for k-sublinear operators with values in the space of measurable functions.
In this paper a posteriori error estimates were established for time-dependent convection diffusion optimal control problems by the elliptic reconstruction technique.
The dual mixed finite element approximation of unilateral contact problems has been studied by Wang and Yang (2009), a priori error estimates have been established for both conforming and nonconforming finite element approximations based on the dual mixed variational formulation with three unknowns, and a Uzawa type iterative algorithm was developed to solve the resulting linear system.
The usefulness of CS estimates has been established for many solid malignancies including urothelial, colorectal, thyroid, ovary, breast, lung and gastric tumors [ 3, 4, 6– 15].
Adjusted RR estimates were further established for predefined follow-up intervals, i.e. the first 3 months, 3 months to 2 years, 2 to 8 years, and longer than 8 years, using an extended Cox model including time-dependent covariates.
