Well-Posedness in Hölder Spaces of Elliptic Differential and Difference Equations

@inproceedings{Ashyralyev2014WellPosednessIH,
  title={Well-Posedness in H{\"o}lder Spaces of Elliptic Differential and Difference Equations},
  author={Allaberen Ashyralyev},
  booktitle={FDM},
  year={2014}
}
In the present paper the well-posedness of the elliptic differential equation $$\begin{aligned} -u^{\prime \prime }(t)+Au(t)=f(t)(-\infty <t<\infty ) \end{aligned}$$ in an arbitrary Banach space E with the general positive operator in Ho lder spaces \(C^{\beta }(\mathbb {R},E_{\alpha })\) is established. The exact estimates in Holder norms for the solution of the problem for elliptic equations are obtained. The high order of accuracy two-step difference schemes generated by an exact… CONTINUE READING