Elliptic operators on refined Sobolev scales on vector bundles

Tetiana Zinchenko. "Elliptic operators on refined Sobolev scales on vector bundles." Open Mathematics 15.1 (2017): 907-925. <http://eudml.org/doc/288316>.

@article{TetianaZinchenko2017,
abstract = {We introduce a refined Sobolev scale on a vector bundle over a closed infinitely smooth manifold. This scale consists of inner product Hörmander spaces parametrized with a real number and a function varying slowly at infinity in the sense of Karamata. We prove that these spaces are obtained by the interpolation with a function parameter between inner product Sobolev spaces. An arbitrary classical elliptic pseudodifferential operator acting between vector bundles of the same rank is investigated on this scale. We prove that this operator is bounded and Fredholm on pairs of appropriate Hörmander spaces. We also prove that the solutions to the corresponding elliptic equation satisfy a certain a priori estimate on these spaces. The local regularity of these solutions is investigated on the refined Sobolev scale. We find new sufficient conditions for the solutions to have continuous derivatives of a given order.},
author = {Tetiana Zinchenko},
journal = {Open Mathematics},
keywords = {Elliptic pseudodifferential operator; Vector bundle; Sobolev space; Hörmander space; Interpolation with function parameter; Fredholm property; A priori estimate of solutions; Regularity of solutions},
language = {eng},
number = {1},
pages = {907-925},
title = {Elliptic operators on refined Sobolev scales on vector bundles},
url = {http://eudml.org/doc/288316},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Tetiana Zinchenko
TI - Elliptic operators on refined Sobolev scales on vector bundles
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 907
EP - 925
AB - We introduce a refined Sobolev scale on a vector bundle over a closed infinitely smooth manifold. This scale consists of inner product Hörmander spaces parametrized with a real number and a function varying slowly at infinity in the sense of Karamata. We prove that these spaces are obtained by the interpolation with a function parameter between inner product Sobolev spaces. An arbitrary classical elliptic pseudodifferential operator acting between vector bundles of the same rank is investigated on this scale. We prove that this operator is bounded and Fredholm on pairs of appropriate Hörmander spaces. We also prove that the solutions to the corresponding elliptic equation satisfy a certain a priori estimate on these spaces. The local regularity of these solutions is investigated on the refined Sobolev scale. We find new sufficient conditions for the solutions to have continuous derivatives of a given order.
LA - eng
KW - Elliptic pseudodifferential operator; Vector bundle; Sobolev space; Hörmander space; Interpolation with function parameter; Fredholm property; A priori estimate of solutions; Regularity of solutions
UR - http://eudml.org/doc/288316
ER -