On relationship between the resolvent convergence and the smoothness of solutions to boundary value problems
Eurasian mathematical journal, Tome 7 (2016) no. 3, pp. 100-103.

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Relationship between the resolvent convergence property and the smoothness of solutions to boundary value problems are studied. The results use pointwise multipliers and $B$-spaces.
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I. V. Tsylin. On relationship between the resolvent convergence and the smoothness of solutions to boundary value problems. Eurasian mathematical journal, Tome 7 (2016) no. 3, pp. 100-103. http://geodesic.mathdoc.fr/item/EMJ_2016_7_3_a8/

[1] M. S. Agranovich, Sobolev spaces, their generalizations, and elliptic problems in domains with smooth and Lipschitz boundary, M., 2013 (in Russian)

[2] G. Barbatis, P. D. Lamberti, “Spectral stability estimates for elliptic operators subject to domain transformations with non-uniformly bounded gradients”, Mathematika, 58:2 (2012), 324–348 | DOI | MR | Zbl

[3] G. Birkhoff, C. de Boor, B. Swartz, B. Wendroff, “Rayleigh–Ritz approximation by piecewise cubic polynomials”, SIAM J. Numer. Anal., 3 (1966), 188–203 | DOI | MR | Zbl

[4] V. I. Burenkov, E. B. Davies, “Spectral stability of the Neumann Laplacian”, J. Differential Equations, 186:2 (2002), 485–508 | DOI | MR | Zbl

[5] V. I. Burenkov, P. D. Lamberti, “Spectral stability of higher order uniformly elliptic operators”, Sobolev spaces in mathematics II, International Mathematical Series, 9, 2009, 69–102 | DOI | MR | Zbl

[6] V. I. Burenkov, P. D. Lamberti, M. Lanza de Cristoforis, “Spectral stability of nonnegative selfadjoint operators”, J. Math. Sci. (N. Y.), 149:4 (2008), 417–452 | DOI | MR

[7] E. Feleqi, “Estimates for the deviation of solutions and eigenfunctions of second-order elliptic Dirichlet boundary value problems under domain perturbation”, Journal of Differential Equations, 260:4 (2016), 3448–3476 | DOI | MR | Zbl

[8] M. I. Neiman-Zade, A. A. Shkalikov, “Schrödinger operators with singular potentials from spaces of multipliers”, Math. Notes, 66:5 (1999), 599–607 | DOI | MR

[9] G. Savaré, “Regularity results for elliptic equations in Lipschitz domains”, J. Funct. Anal., 152 (1998), 176–201 | DOI | MR | Zbl

[10] A. M. Stepin, I. V. Tsylin, “On boundary value problems for elliptic operators in the case of domains on manifolds”, Doklady Mathematics, 92:1 (2015), 428–432 | DOI | MR | Zbl

[11] I. V. Tsylin, “On the smoothness of solutions to elliptic equations in domains with Hölder boundary”, Eurasian Math. J., 6:3 (2015), 76–92 | MR