Anop, Anna A.; Murach, Aleksandr A. Parameter-elliptic problems and interpolation with a function parameter. (English) Zbl 1313.35092 Methods Funct. Anal. Topol. 20, No. 2, 103-116 (2014). 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. Reviewer: Anatoly N. Kochubei (Kyïv) Cited in 5 Documents 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 Keywords:parameter-elliptic problems; interpolation with functional parameter; extended Sobolev scale; Hörmander spaces Citations:Zbl 1224.35101; Zbl 1294.46036 × Cite Format Result Cite Review PDF Full Text: arXiv