Geodesic
On the Closure of Smooth Compactly Supported Functions in Weighted H\"older Spaces
Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 616-631.

Voir la notice de l'article provenant de la source Math-Net.Ru

The closure of the set of smooth compactly supported functions in a weighted Hölder space on $\mathbb R^n$, $n\ge 1$, with a weight controlling the behavior at the point at infinity is described. As an application, a solvability criterion for operator equations generated by de Rham differentials both in these spaces and on the closure of the set of smooth compactly supported functions in them for $n\ge 2$ is obtained.
Keywords: weighted Hölder spaces, de Rham complex. 
@article{MZM_2019_105_4_a11,
     author = {K. V. Sidorova (Gagelgans) and A. A. Shlapunov},
     title = {On the {Closure} of {Smooth} {Compactly} {Supported} {Functions} in {Weighted} {H\"older} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {616--631},
     publisher = {mathdoc},
     volume = {105},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a11/}
}
TY  - JOUR
AU  - K. V. Sidorova (Gagelgans)
AU  - A. A. Shlapunov
TI  - On the Closure of Smooth Compactly Supported Functions in Weighted H\"older Spaces
JO  - Matematičeskie zametki
PY  - 2019
SP  - 616
EP  - 631
VL  - 105
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a11/
LA  - ru
ID  - MZM_2019_105_4_a11
ER  - 
%0 Journal Article
%A K. V. Sidorova (Gagelgans)
%A A. A. Shlapunov
%T On the Closure of Smooth Compactly Supported Functions in Weighted H\"older Spaces
%J Matematičeskie zametki
%D 2019
%P 616-631
%V 105
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a11/
%G ru
%F MZM_2019_105_4_a11
K. V. Sidorova (Gagelgans); A. A. Shlapunov. On the Closure of Smooth Compactly Supported Functions in Weighted H\"older Spaces. Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 616-631. http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a11/

[1] N. M. Gunther, La théorie du potentiel et ses applications aux problémes fondamentaux de la physique mathématique, Gauthier-Villars, Paris, 1934 | Zbl

[2] D. Gilbarg, N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983 | MR | Zbl

[3] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR | Zbl

[4] S. Krantz, “Intrinsic Lipschitz classes on manifolds with applications to complex function theory and estimates for the $\overline \partial$ and $\overline \partial_b$ equations”, Manuscripta Math., 24:4 (1978), 351–378 | DOI | MR | Zbl

[5] R. McOwen, “Behavior of the Laplacian on weighted Sobolev spaces”, Comm. Pure Appl. Math., 32:6 (1979), 783–795 | DOI | MR | Zbl

[6] O. A. Ladyzhenskaya, Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970 | MR | Zbl

[7] V. Mazya, J. Rossmann, “Schauder estimates for solutions to boundary value problems for second order elliptic systems in polyhedral domains”, Appl. Anal., 83:3 (2004), 271–308 | DOI | MR | Zbl

[8] V. A. Kondratev, “Kraevye zadachi dlya parabolicheskikh uravnenii v zamknutykh oblastyakh”, Tr. MMO, 15, Izd-vo Mosk. un-ta, M., 1966, 400–451 | MR | Zbl

[9] L. Hörmander, The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis, Springer-Verlag, Berlin, 1983 | MR | Zbl

[10] N. N. Tarkhanov, Metod parametriksa v teorii differentsialnykh kompleksov, Nauka, Novosibirsk, 1990 | MR

[11] T. Behrndt, “On the Cauchy problem for the heat equation on Riemannian manifolds with conical singularities”, Q. J. Math., 64:4 (2011), 981–1007 | DOI | MR

[12] L. Nirenberg, H. Walker, “The null spaces of elliptic partial differential operators in $\mathbb R^n$”, J. Math. Anal. Appl., 42 (1973), 271–301 | DOI | MR | Zbl

[13] A. A. Shlapunov, “O zadache Koshi dlya uravneniya Laplasa”, Sib. matem. zhurn., 33:3 (1992), 205–215 | Zbl