Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
A priori estimates near the boundary for the solutions of non-diagonal elliptic systems with strong non-linearity. / Arkhipova, A. A.
в: Izvestiya RAN, ser. Matematika, Том 68, № 2, 01.03.2004, стр. 243-258.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - A priori estimates near the boundary for the solutions of non-diagonal elliptic systems with strong non-linearity
AU - Arkhipova, A. A.
PY - 2004/3/1
Y1 - 2004/3/1
N2 - We consider quasilinear elliptic non-diagonal systems of equations with strong non-linearity with respect to the gradient. We have already shown that the generalized solution of this problem is Hölder continuous in the neighbourhood of points of the domain at which the norm of the gradient of the solution is sufficiently small in the Morrey space L 2,n-2. We estimate the Hölder norm of the solution in the neighbourhood of such points in terms of its norm in the Sobolev space W 2 1. We obtain a similar result under the Dirichlet boundary condition for points situated in the neighbourhood of the boundary.
AB - We consider quasilinear elliptic non-diagonal systems of equations with strong non-linearity with respect to the gradient. We have already shown that the generalized solution of this problem is Hölder continuous in the neighbourhood of points of the domain at which the norm of the gradient of the solution is sufficiently small in the Morrey space L 2,n-2. We estimate the Hölder norm of the solution in the neighbourhood of such points in terms of its norm in the Sobolev space W 2 1. We obtain a similar result under the Dirichlet boundary condition for points situated in the neighbourhood of the boundary.
UR - http://www.scopus.com/inward/record.url?scp=33746543131&partnerID=8YFLogxK
U2 - 10.1070/IM2004v068n02ABEH000473
DO - 10.1070/IM2004v068n02ABEH000473
M3 - Article
AN - SCOPUS:33746543131
VL - 68
SP - 243
EP - 258
JO - Izvestiya Mathematics
JF - Izvestiya Mathematics
SN - 1064-5632
IS - 2
ER -
ID: 15728885