Elliptic operators on refined Sobolev scales on vector bundles

• Autorzy: Tetiana Zinchenko
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Elliptic pseudodifferential operator; Vector bundle; Sobolev space; Hörmander space; Interpolation with function parameter; Fredholm property; A priori estimate of solutions; Regularity of solutions

Kategorie tematyczne

• 58J05: Elliptic equations on manifolds, general theory
• 46B70: Interpolation between normed linear spaces
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 35J48: Higher-order elliptic systems

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 907-925

Daty

wydano

2017-01-01

otrzymano

2016-11-29

zaakceptowano

2017-05-29

online

2017-07-13

Twórcy

autor

Tetiana Zinchenko

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Identyfikatory

DOI

10.1515/math-2017-0076