Geodesic
A boundary-value problem in weighted Hölder spaces for elliptic equations which degenerate at the boundary of the domain
Sbornik. Mathematics, Tome 204 (2013) no. 7, pp. 958-978 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An elliptic boundary-value problem for second-order equations with nonnegative characteristic form is investigated in the situation when there is a weak degeneracy on the boundary of the domain. A priori estimates are obtained for solutions and the problem is proved to be solvable in some weighted Hölder spaces. Bibliography: 18 titles.
Keywords: degenerate elliptic equation, a priori estimate.
Mots-clés : weighted Hölder spaces 
@article{SM_2013_204_7_a1,
     author = {B. V. Bazalii and S. P. Degtyarev},
     title = {A boundary-value problem in weighted {H\"older} spaces for elliptic equations which degenerate at the boundary of the domain},
     journal = {Sbornik. Mathematics},
     pages = {958--978},
     year = {2013},
     volume = {204},
     number = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_7_a1/}
}
TY  - JOUR
AU  - B. V. Bazalii
AU  - S. P. Degtyarev
TI  - A boundary-value problem in weighted Hölder spaces for elliptic equations which degenerate at the boundary of the domain
JO  - Sbornik. Mathematics
PY  - 2013
SP  - 958
EP  - 978
VL  - 204
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/SM_2013_204_7_a1/
LA  - en
ID  - SM_2013_204_7_a1
ER  - 
%0 Journal Article
%A B. V. Bazalii
%A S. P. Degtyarev
%T A boundary-value problem in weighted Hölder spaces for elliptic equations which degenerate at the boundary of the domain
%J Sbornik. Mathematics
%D 2013
%P 958-978
%V 204
%N 7
%U http://geodesic.mathdoc.fr/item/SM_2013_204_7_a1/
%G en
%F SM_2013_204_7_a1
B. V. Bazalii; S. P. Degtyarev. A boundary-value problem in weighted Hölder spaces for elliptic equations which degenerate at the boundary of the domain. Sbornik. Mathematics, Tome 204 (2013) no. 7, pp. 958-978. http://geodesic.mathdoc.fr/item/SM_2013_204_7_a1/

[1] O. A. Oleinik, E. V. Radkevich, “Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Itogi nauki. Ser. Matematika. Mat. anal. 1969, VINITI, M., 1971, 7–252 | MR | Zbl

[2] M. V. Keldysh, “O nekotorykh sluchayakh vyrozhdeniya uravneniya ellipticheskogo tipa na granitse oblasti”, DAN SSSR, 77:2 (1951), 181–183 | MR

[3] G. Fickera, “Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine”, Atti Accad. Naz. Lincei. Mem. Cl. Sci. Fis. Mat. Nat. Sez. I (8), 5:1 (1956), 3–30 | MR | Zbl

[4] M. Visik, “Boundary-value problems for elliptic equations degenerating on the boundary of a region”, Amer. Math. Soc. Transl. Ser. 2, 35 (1964), 15–78 | MR | Zbl | Zbl

[5] M. I. Vishik, O. A. Ladyzhenskaya, “Boundary value problems for partial differential equations and certain classes of operator equations”, Amer. Math. Soc. Transl. Ser. 2, 10 (1958), 223–281 | MR | Zbl | Zbl

[6] O. A. Oleinik, “O lineinykh uravneniyakh vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Matem. sb., 69(111):1 (1966), 111–140 | MR | Zbl

[7] M. I. Višik, V. V. Grušin, “Boundary value problems for partial differential equations and certain classes of operator equations”, Math. USSR-Sb., 9:4 (1969), 423–454 | DOI | MR | Zbl | Zbl

[8] O. A. Oleinik, E. V. Radkevich, Uravneniya s neotritsatelnoi kharakteristicheskoi formoi, Izd-vo Mosk. un-ta, M., 2010

[9] S. Levendorskii, Degenerate elliptic equations, Math. Appl., 258, Kluwer Acad. Publ., Dordrecht, 1993 | MR

[10] C. Goulaouic, N. Shimakura, “Regularié hölderienne de certains problèmes aux limites elliptiques dégénérés”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 10:1 (1983), 79–108 | MR | Zbl

[11] B. V. Bazalii, S. P. Degtyarev, “On a boundary value problem for a strongly degenerate second order elliptic equation in an angular domain”, Ukrainian Math. J., 59:7 (2007), 955-975 | DOI | MR | Zbl

[12] S. P. Degtyarev, “On the optimal regularity of solutions of the first boundary value problem for a class of degenerate elliptic equations”, Ukr. Math. Bull., 3:4 (2006), 423-446 | MR | Zbl

[13] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Ural'tseva, Linear and quasi-linear equations of parabolic type, Transl. Math. Monogr., 23, Amer. Math. Soc., Providence, RI, 1968 | MR | MR | Zbl | Zbl

[14] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Math. Ser., 30, Princeton Univ. Press, Princeton, NJ, 1970 | MR | MR | Zbl | Zbl

[15] A. Lunardi, Analytic semigroups and optimal regularity in parabolic problems, Progr. Nonlinear Differential Equations Appl., 16, Birkhäuser, Basel, 1995 | MR | Zbl

[16] K. K. Golovkin, “Ob ekvivalentnykh normirovkakh drobnykh prostranstv”, Raboty po avtomaticheskomu programmirovaniyu, chislennym metodam i funktsionalnomu analizu, Tr. MIAN SSSR, 66, Izd-vo AN SSSR, M.–L., 1962, 364–383 | MR | Zbl

[17] O. A. Ladyzhenskaya, N. N. Ural'tseva, Linear and quasilinear elliptic equations, Math. Sci. Engrg., 46, Academic Press, New York–London, 1968 | MR | MR | Zbl | Zbl

[18] D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order, Grundlehren Math. Wiss., 224, Springer-Verlag, Berlin, 1983 | MR | MR | Zbl | Zbl