The elliptic problems in a family of planar open sets

Tami, Abdelkader. "The elliptic problems in a family of planar open sets." Applications of Mathematics 64.5 (2019): 485-499. <http://eudml.org/doc/294149>.

@article{Tami2019,
abstract = {We propose, on a model case, a new approach to classical results obtained by V. A. Kondrat'ev (1967), P. Grisvard (1972), (1985), H. Blum and R. Rannacher (1980), V. G. Maz'ya (1980), (1984), (1992), S. Nicaise (1994a), (1994b), (1994c), M. Dauge (1988), (1990), (1993a), (1993b), A. Tami (2016), and others, describing the singularities of solutions of an elliptic problem on a polygonal domain of the plane that may appear near a corner. It provides a more precise description of how the solutions decompose, puts into evidence the analogy of such decompositions with standard Taylor expansions, and gives uniform estimates with respect to the angle parameter. This last property allows the treatment of families of elliptic problems on families of open sets.},
author = {Tami, Abdelkader},
journal = {Applications of Mathematics},
keywords = {biharmonic operator; elliptic problems; nonsmooth boundaries; uniform singularity estimates; Sobolev spaces},
language = {eng},
number = {5},
pages = {485-499},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The elliptic problems in a family of planar open sets},
url = {http://eudml.org/doc/294149},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Tami, Abdelkader
TI - The elliptic problems in a family of planar open sets
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 5
SP - 485
EP - 499
AB - We propose, on a model case, a new approach to classical results obtained by V. A. Kondrat'ev (1967), P. Grisvard (1972), (1985), H. Blum and R. Rannacher (1980), V. G. Maz'ya (1980), (1984), (1992), S. Nicaise (1994a), (1994b), (1994c), M. Dauge (1988), (1990), (1993a), (1993b), A. Tami (2016), and others, describing the singularities of solutions of an elliptic problem on a polygonal domain of the plane that may appear near a corner. It provides a more precise description of how the solutions decompose, puts into evidence the analogy of such decompositions with standard Taylor expansions, and gives uniform estimates with respect to the angle parameter. This last property allows the treatment of families of elliptic problems on families of open sets.
LA - eng
KW - biharmonic operator; elliptic problems; nonsmooth boundaries; uniform singularity estimates; Sobolev spaces
UR - http://eudml.org/doc/294149
ER -