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
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/
@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

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We prove local (in time) unique solvability of the nonlinear Amann problem in Hölder spaces of functions. Solution estimates are obtained in these spaces.

[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