Regular Elliptic Boundary-Value Problems in the Extended Sobolev Scale
AbstractWe investigate an arbitrary regular elliptic boundary-value problem given in a bounded Euclidean C ∞- domain. It is shown that the operator of the problem is bounded and Fredholm in appropriate pairs of Hörmander inner-product spaces. They are parametrized with the help of an arbitrary radial function RO-varying at ∞ and form the extended Sobolev scale. We establish a priori estimates for the solutions of the problem and study their local regularity on this scale. New sufficient conditions for the generalized partial derivatives of the solutions to be continuous are obtained.
How to Cite
AnopA. V., and MurachA. A. “Regular Elliptic Boundary-Value Problems in the Extended Sobolev Scale”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 7, July 2014, pp. 867–883, http://umj.imath.kiev.ua/index.php/umj/article/view/2185.