## Parameter-elliptic problems and interpolation with a function parameter.(English)Zbl 1313.35092

The extended Sobolev scale consists of all those Hilbert spaces that are interpolation spaces with respect to the classical Sobolev scale. These spaces are the Hörmander spaces $$B_{2,k}$$ for which the smoothness index $$k$$ is an arbitrary radial function RO-varying at infinity; see the papers by A. A. Murach [Ukr. Math. J. 61, No. 3, 467–477 (2009; Zbl 1224.35101)]; V. A. Mikhailets and A. A. Murach [Ukr. Math. J. 65, No. 3, 435–447 (2013; Zbl 1294.46036)] devoted to elliptic operators and systems considered on this scale.
In the paper under review, the authors investigate parameter-elliptic boundary value problems on the extended scale. It is proved that the corresponding operators are isomorphisms provided the absolute value of the parameter is large enough. Two-sided estimates of solutions are obtained.

### MSC:

 35J40 Boundary value problems for higher-order elliptic equations 46B70 Interpolation between normed linear spaces 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

### Citations:

Zbl 1224.35101; Zbl 1294.46036
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