Geodesic
The solvability of the first initial-boundary problem for parabolic and degenerate parabolic equations in domains with a~conical point
Sbornik. Mathematics, Tome 201 (2010) no. 7, pp. 999-1028

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

The first initial-boundary problem for second-order parabolic and degenerate parabolic equations is investigated in a domain with a conical or angular point. The means of attack is already known and uses weighted classes of smooth or integrable functions. Sufficient conditions for a unique solution to exist and for coercive estimates for the solution to be obtained are formulated in terms of the angular measure of the solid angle and the exponent of the weight. It is also shown that if these conditions fail to hold, then the parabolic problem has elliptic properties, that is, it can have a nonzero kernel or can be nonsolvable, and, in the latter case, it is not even a Fredholm problem. A parabolic equation and an equation with some degeneracy or a singularity at a conical point are considered. Bibliography: 49 titles.
Keywords: irregular domain, coercive estimate, spectral properties.
Mots-clés : parabolic equation 
@article{SM_2010_201_7_a3,
     author = {S. P. Degtyarev},
     title = {The solvability of the first initial-boundary problem for parabolic and degenerate parabolic equations in domains with a~conical point},
     journal = {Sbornik. Mathematics},
     pages = {999--1028},
     publisher = {mathdoc},
     volume = {201},
     number = {7},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_7_a3/}
}
TY  - JOUR
AU  - S. P. Degtyarev
TI  - The solvability of the first initial-boundary problem for parabolic and degenerate parabolic equations in domains with a~conical point
JO  - Sbornik. Mathematics
PY  - 2010
SP  - 999
EP  - 1028
VL  - 201
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2010_201_7_a3/
LA  - en
ID  - SM_2010_201_7_a3
ER  - 
%0 Journal Article
%A S. P. Degtyarev
%T The solvability of the first initial-boundary problem for parabolic and degenerate parabolic equations in domains with a~conical point
%J Sbornik. Mathematics
%D 2010
%P 999-1028
%V 201
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2010_201_7_a3/
%G en
%F SM_2010_201_7_a3
S. P. Degtyarev. The solvability of the first initial-boundary problem for parabolic and degenerate parabolic equations in domains with a~conical point. Sbornik. Mathematics, Tome 201 (2010) no. 7, pp. 999-1028. http://geodesic.mathdoc.fr/item/SM_2010_201_7_a3/