On the Heumann problem for second order elliptic equations in domains with edges at the boundary
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 15, Tome 127 (1983), pp. 7-48
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It is proved that a weak solution of the Heumann problem for a second order elliptic equation in the a domain $\Omega\subset\mathbb R^n$ with smooth non-intersecting $n-2$-dimensional edges at the boundary belongs to a certain weighted Sobolev space Coercive estimates of the solution in the norm of this space are established.
@article{ZNSL_1983_127_a1,
author = {W. M. Zaj\k{a}czkowski and V. A. Solonnikov},
title = {On the {Heumann} problem for second order elliptic equations in domains with edges at the boundary},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {7--48},
publisher = {mathdoc},
volume = {127},
year = {1983},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_127_a1/}
}
TY - JOUR AU - W. M. Zajączkowski AU - V. A. Solonnikov TI - On the Heumann problem for second order elliptic equations in domains with edges at the boundary JO - Zapiski Nauchnykh Seminarov POMI PY - 1983 SP - 7 EP - 48 VL - 127 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1983_127_a1/ LA - ru ID - ZNSL_1983_127_a1 ER -
%0 Journal Article %A W. M. Zajączkowski %A V. A. Solonnikov %T On the Heumann problem for second order elliptic equations in domains with edges at the boundary %J Zapiski Nauchnykh Seminarov POMI %D 1983 %P 7-48 %V 127 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1983_127_a1/ %G ru %F ZNSL_1983_127_a1
W. M. Zajączkowski; V. A. Solonnikov. On the Heumann problem for second order elliptic equations in domains with edges at the boundary. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 15, Tome 127 (1983), pp. 7-48. http://geodesic.mathdoc.fr/item/ZNSL_1983_127_a1/