Displaying similar documents to “Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold”

Elliptic operators on refined Sobolev scales on vector bundles

Tetiana Zinchenko (2017)

Open Mathematics

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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...

Solvability conditions for elliptic problems with non-Fredholm operators

V. Volpert, B. Kaźmierczak, M. Massot, Z. Peradzyński (2002)

Applicationes Mathematicae

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The paper is devoted to solvability conditions for linear elliptic problems with non-Fredholm operators. We show that the operator becomes normally solvable with a finite-dimensional kernel on properly chosen subspaces. In the particular case of a scalar equation we obtain necessary and sufficient solvability conditions. These results are used to apply the implicit function theorem for a nonlinear elliptic problem; we demonstrate the persistence of travelling wave solutions to spatially...