Geodesic
Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains
Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 245-254.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We consider a class of semilinear elliptic problems in two- and three-dimensional domains with conical points. We introduce Sobolev spaces with detached asymptotics generated by the asymptotical behaviour of solutions of corresponding linearized problems near conical boundary points. We show that the corresponding nonlinear operator acting between these spaces is Frechet differentiable. Applying the local invertibility theorem we prove that the solution of the semilinear problem has the same asymptotic behaviour near the conical points as the solution of the linearized problem if the norms of the given right hand sides are small enough. Estimates for the difference between the solution of the semilinear and of the linearized problem are derived.
DOI : 10.21136/MB.1999.126247
Classification : 35A07, 35B65, 35C20, 35J60
Keywords: semilinear elliptic problems; spaces with detached asymptotics; asymptotic behaviour near conical points 
@article{10_21136_MB_1999_126247,
     author = {Bochniak, M. and S\"andig, A.-M.},
     title = {Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains},
     journal = {Mathematica Bohemica},
     pages = {245--254},
     publisher = {mathdoc},
     volume = {124},
     number = {2-3},
     year = {1999},
     doi = {10.21136/MB.1999.126247},
     mrnumber = {1780695},
     zbl = {0937.35003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126247/}
}
TY  - JOUR
AU  - Bochniak, M.
AU  - Sändig, A.-M.
TI  - Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains
JO  - Mathematica Bohemica
PY  - 1999
SP  - 245
EP  - 254
VL  - 124
IS  - 2-3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126247/
DO  - 10.21136/MB.1999.126247
LA  - en
ID  - 10_21136_MB_1999_126247
ER  - 
%0 Journal Article
%A Bochniak, M.
%A Sändig, A.-M.
%T Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains
%J Mathematica Bohemica
%D 1999
%P 245-254
%V 124
%N 2-3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126247/
%R 10.21136/MB.1999.126247
%G en
%F 10_21136_MB_1999_126247
Bochniak, M.; Sändig, A.-M. Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains. Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 245-254. doi : 10.21136/MB.1999.126247. http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126247/

Cité par Sources :