Geodesic
Mixed problems with non-homogeneous boundary conditions in Lipschitz domains for second-order elliptic equations with a~parameter
Sbornik. Mathematics, Tome 187 (1996) no. 4, pp. 525-580

Voir la notice de l'article provenant de la source Math-Net.Ru

For a second-order elliptic equation involving a parameter, with principal part in divergence form in Lipschitz domain $\Omega$ mixed problems (of Zaremba type) with non-homogeneous boundary conditions are considered for generalized functions in $W^1_2(\Omega )$. The Poincaré–Steklov operators on Lipschitz piece $\gamma$ of the domain's boundary $\Gamma$ corresponding to homogeneous mixed boundary conditions on $\Gamma \setminus \gamma$ are studied. For a homogeneous equation with separation of variables in a tube domain with Lipschitz section, the Fourier method is substantiated for homogeneous mixed boundary conditions on the lateral surface and non-homogeneous conditions on the ends. 
@article{SM_1996_187_4_a2,
     author = {B. V. Pal'tsev},
     title = {Mixed problems with non-homogeneous boundary conditions in {Lipschitz} domains for second-order elliptic equations with a~parameter},
     journal = {Sbornik. Mathematics},
     pages = {525--580},
     publisher = {mathdoc},
     volume = {187},
     number = {4},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_4_a2/}
}
TY  - JOUR
AU  - B. V. Pal'tsev
TI  - Mixed problems with non-homogeneous boundary conditions in Lipschitz domains for second-order elliptic equations with a~parameter
JO  - Sbornik. Mathematics
PY  - 1996
SP  - 525
EP  - 580
VL  - 187
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1996_187_4_a2/
LA  - en
ID  - SM_1996_187_4_a2
ER  - 
%0 Journal Article
%A B. V. Pal'tsev
%T Mixed problems with non-homogeneous boundary conditions in Lipschitz domains for second-order elliptic equations with a~parameter
%J Sbornik. Mathematics
%D 1996
%P 525-580
%V 187
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1996_187_4_a2/
%G en
%F SM_1996_187_4_a2
B. V. Pal'tsev. Mixed problems with non-homogeneous boundary conditions in Lipschitz domains for second-order elliptic equations with a~parameter. Sbornik. Mathematics, Tome 187 (1996) no. 4, pp. 525-580. http://geodesic.mathdoc.fr/item/SM_1996_187_4_a2/