Geodesic
On the smoothness of solutions of differential equations at singular points of the boundary of the domain
Izvestiya. Mathematics, Tome 37 (1991) no. 3, pp. 489-510 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Second-order elliptic equations with analytic coefficients and right sides in a domain with piecewise smooth boundary are studied. It is assumed that the boundary is characteristic at all points. Both Lipschitz and non-Lipschitz singularities of the boundary are admitted. It is proved that for large values of the spectral parameter, solutions possess high smoothness even at those points where the boundary has singularities. The results are based on the study of a constructive representation of solutions of the equations in the form of series of analytic functions. 
@article{IM2_1991_37_3_a1,
     author = {A. V. Babin},
     title = {On the smoothness of solutions of differential equations at singular points of the boundary of the domain},
     journal = {Izvestiya. Mathematics},
     pages = {489--510},
     year = {1991},
     volume = {37},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a1/}
}
TY  - JOUR
AU  - A. V. Babin
TI  - On the smoothness of solutions of differential equations at singular points of the boundary of the domain
JO  - Izvestiya. Mathematics
PY  - 1991
SP  - 489
EP  - 510
VL  - 37
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a1/
LA  - en
ID  - IM2_1991_37_3_a1
ER  - 
%0 Journal Article
%A A. V. Babin
%T On the smoothness of solutions of differential equations at singular points of the boundary of the domain
%J Izvestiya. Mathematics
%D 1991
%P 489-510
%V 37
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a1/
%G en
%F IM2_1991_37_3_a1
A. V. Babin. On the smoothness of solutions of differential equations at singular points of the boundary of the domain. Izvestiya. Mathematics, Tome 37 (1991) no. 3, pp. 489-510. http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a1/

[1] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. Mosk. matem. obschestva, 16, 1967, 209–292

[2] Kondratev V. A., “O gladkosti resheniya zadachi Dirikhle dlya ellipticheskikh uravnenii vtorogo poryadka v kusochno gladkoi oblasti”, Differents. uravn., 6:10 (1970), 1829–1843

[3] Kondratev V. A., Oleinik O. A., “Kraevye zadachi dlya uravnenii s chastnymi proizvodnymi v negladkikh oblastyakh”, UMN, 38:2 (1983), 3–76 | MR

[4] Rempel S., Schulze B.-W., “Branching of asymptotics for elliptic operators on manifolds with wedges”, Partial Diff. Equ., Banach Center Publ., 19, 1984.

[5] Melrose R. B., Pseudodifferential operators on manifolds with corners Massachusetts, Institute of Technology, 1987

[6] Oleinik O. A., Radkevich E. V., “Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Itogi nauki. Matem. analiz 1969, VINITI, M., 1971, 7–252 | MR | Zbl

[7] Kohn J. J., Nirenberg L., “Non-coercitive boundary value problems”, Comm. Pure Appl. Math., 18:3 (1965), 443–492 | DOI | MR | Zbl

[8] Baouendy M. S., Goulaouic C., “Regularite analitique et itérés d'operateurs elliptiques degeneres”, J. Funct. Anal., 9 (1972), 208–248 | DOI | MR

[9] Babin A. V., “Postroenie i issledovanie reshenii differentsialnykh uravnenii metodami teorii priblizheniya funktsii”, Matem. sb., 123:2 (1984), 147–173 | MR | Zbl

[10] Babin A. V., “O svyazi analiticheskikh svoistv operatornykh funktsii i gladkosti reshenii vyrozhdayuschikhsya differentsialnykh uravnenii”, Funktsion. analiz i ego pril., 22:1 (1988), 60–61 | MR | Zbl

[11] Babin A. V., Iterations of differential operators, Gordon and Breach, N.Y., 1989 | MR | Zbl

[12] Babin A. V., “O polinomialnoi razreshimosti differentsialnykh uravnenii s koeffitsientami iz klassov beskonechno differentsiruemykh funktsii”, Matem. zametki, 34:2 (1983), 249–260 | MR