On solvability of H. Amann's problem in Hölder spaces
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 33, Tome 295 (2003), pp. 18-56 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We prove local (in time) unique solvability of the nonlinear Amann problem in Hölder spaces of functions. Solution estimates are obtained in these spaces.
@article{ZNSL_2003_295_a1,
     author = {G. I. Bizhanova},
     title = {On solvability of {H.~Amann's} problem in {H\"older} spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {18--56},
     year = {2003},
     volume = {295},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_295_a1/}
}
TY  - JOUR
AU  - G. I. Bizhanova
TI  - On solvability of H. Amann's problem in Hölder spaces
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 18
EP  - 56
VL  - 295
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_295_a1/
LA  - ru
ID  - ZNSL_2003_295_a1
ER  - 
%0 Journal Article
%A G. I. Bizhanova
%T On solvability of H. Amann's problem in Hölder spaces
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 18-56
%V 295
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_295_a1/
%G ru
%F ZNSL_2003_295_a1
G. I. Bizhanova. On solvability of H. Amann's problem in Hölder spaces. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 33, Tome 295 (2003), pp. 18-56. http://geodesic.mathdoc.fr/item/ZNSL_2003_295_a1/

[1] H. Amann, “Nonhomogeneous linear and quasi-linear elliptic and parabolic boundary value problems”, Function Spaces, Differential Operator and Nonlinear Analysis, 133, Teubner-Texte zur Math., Stuttgart-Leipzig, 1993, 9–126 | MR | Zbl

[2] H. Amann, M. Renardy, “Reaction-diffusion problems in electrolysis”, NoDEA, 1 (1994), 91–117 | DOI | MR | Zbl

[3] S. N. Pokhozhaev, “Ob odnoi nelineinoi ellipticheskoi zadache G. Amanna”, Diff. uravn., 30:4 (1994), 675–691 | MR | Zbl

[4] H. Amann, Linear and quasi-linear parabolic problems, V. I, Monographs in Mathematics, 89, Birkhauser Verlag, Basel, Boston, Berlin, 1995 | MR | Zbl

[5] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR

[6] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[7] D. Gilbarg, N. Trudinger, Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[8] S. G. Mikhlin, Lineinye uravneniya v chastnykh proizvodnykh, Vyssh. shkola, M., 1977 | MR

[9] G. I. Bizhanova, “Issledovanie razreshimosti mnogomernykh dvukhfaznykh zadach Stefana i nestatsionarnoi filtratsii Florina dlya parabolicheskikh uravnenii vtorogo poryadka v vesovykh gelderovskikh prostranstvakh funktsii”, Zap. nauchn. semin. POMI, 213, 1994, 14–47 | MR

[10] A. I. Maltsev, Osnovy lineinoi algebry, Nauka, M., 1970