Geodesic
A boundary value problem with degeneration on the boundary along the manifold of codimension $k > 2$
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 2, pp. 7-10 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article considers the boundary value problem for elliptic equations of arbitrary order $2m$ with degeneracy on the boundary of the domain along manifolds of codimension $k > 2$. The study uses methods of functional analysis and geometry of smooth manifolds proposed by Y. V. Egorov and V. A. Kondratiev. These methods allow us to investigate the boundary value problem in more general formulation. Aprioristic estimates for the solution of a task in the generalized spaces of Sobolev – Slobodetsky are obtained and the theorem of smoothness of solutions of a task is formulated.
Keywords: elliptic operators, smooth variety, condition Lopatinsky.
Mots-clés : transformation Fourier 
@article{SVMO_2016_18_2_a0,
     author = {D. I. Boyarkin},
     title = {A boundary value problem with degeneration on the boundary along the manifold of codimension $k > 2$},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {7--10},
     year = {2016},
     volume = {18},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2016_18_2_a0/}
}
TY  - JOUR
AU  - D. I. Boyarkin
TI  - A boundary value problem with degeneration on the boundary along the manifold of codimension $k > 2$
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2016
SP  - 7
EP  - 10
VL  - 18
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SVMO_2016_18_2_a0/
LA  - ru
ID  - SVMO_2016_18_2_a0
ER  - 
%0 Journal Article
%A D. I. Boyarkin
%T A boundary value problem with degeneration on the boundary along the manifold of codimension $k > 2$
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2016
%P 7-10
%V 18
%N 2
%U http://geodesic.mathdoc.fr/item/SVMO_2016_18_2_a0/
%G ru
%F SVMO_2016_18_2_a0
D. I. Boyarkin. A boundary value problem with degeneration on the boundary along the manifold of codimension $k > 2$. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 2, pp. 7-10. http://geodesic.mathdoc.fr/item/SVMO_2016_18_2_a0/

[1] Bitsadze A. V., Kraevye zadachi dlya ellipticheskikh uravnenii vtorogo poryadka, Nauka, M., 1966, 293 pp. | MR

[2] Borrelli R., “The singular, second order oblique derivative problem”, J. Math. and Mech., 1966, 51–81 | MR | Zbl

[3] Boyarkin D. I., “Odno obobschenie zadachi s kosoi proizvodnoi”, UMN, 38:1(229) (1983), 157–158 | MR

[4] Boyarkin D. I., “Neregulyarnaya ellipticheskaya kraevaya zadacha”, Trudy Srednevolzhskogo matematicheskogo obschestva, 10:1 (2008), 119–122 | MR | Zbl

[5] Egorov Yu. V., Lineinye differentsialnye uravneniya glavnogo tipa, Nauka, M., 1984, 360 pp. | MR

[6] Egorov Yu. V., Kondratev V. A., “O zadache s kosoi proizvodnoi”, Matem. sb., 78 (1969), 148–176 | MR | Zbl

[7] Mazya V. G., Paneyakh B. P., “Vyrozhdayuschiesya ellipticheskie operatory i zadacha s kosoi proizvodnoi”, Tr. MMO, 31, 1974, 237–255

[8] Hormander L., “Pseudo-differential operators and non-elliptic boundary problems”, Ann. Math., 83 (1966), 129–209 ; Khërmander L., “Psevdodifferentsialnye operatory i neellipticheskie kraevye zadachi”, Psevdodifferentsialnye operatory, Mir, M., 1967, 166–296 | DOI | MR | Zbl | MR