Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains

M. Bochniak; Anna-Margarete Sändig

Mathematica Bohemica (1999)

  • Volume: 124, Issue: 2-3, page 245-254
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Bochniak, M., and Sändig, Anna-Margarete. "Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains." Mathematica Bohemica 124.2-3 (1999): 245-254. <http://eudml.org/doc/248476>.

@article{Bochniak1999,
abstract = {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.},
author = {Bochniak, M., Sändig, Anna-Margarete},
journal = {Mathematica Bohemica},
keywords = {semilinear elliptic problems; spaces with detached asymptotics; asymptotic behaviour near conical points; semilinear elliptic problems; spaces with detached asymptotics; asymptotic behaviour near conical points},
language = {eng},
number = {2-3},
pages = {245-254},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains},
url = {http://eudml.org/doc/248476},
volume = {124},
year = {1999},
}

TY - JOUR
AU - Bochniak, M.
AU - Sändig, Anna-Margarete
TI - Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains
JO - Mathematica Bohemica
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 124
IS - 2-3
SP - 245
EP - 254
AB - 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.
LA - eng
KW - semilinear elliptic problems; spaces with detached asymptotics; asymptotic behaviour near conical points; semilinear elliptic problems; spaces with detached asymptotics; asymptotic behaviour near conical points
UR - http://eudml.org/doc/248476
ER -

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