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Study of a singular equation set in the half-space

Published online by Cambridge University Press:  20 September 2012

C. Amrouche
Affiliation:
Laboratoire de Mathématiques Appliquées, UMR-CNRS No. 5142, IPRA BP 1155, 64013 Pau Cedex, France (cherif.amrouche@univ-pau.fr; fabien.dahoumane@univ-pau.fr; guy.vallet@univ-pau.fr)
F. Dahoumane
Affiliation:
Laboratoire de Mathématiques Appliquées, UMR-CNRS No. 5142, IPRA BP 1155, 64013 Pau Cedex, France (cherif.amrouche@univ-pau.fr; fabien.dahoumane@univ-pau.fr; guy.vallet@univ-pau.fr)
G. Vallet
Affiliation:
Laboratoire de Mathématiques Appliquées, UMR-CNRS No. 5142, IPRA BP 1155, 64013 Pau Cedex, France (cherif.amrouche@univ-pau.fr; fabien.dahoumane@univ-pau.fr; guy.vallet@univ-pau.fr)

Abstract

This work is dedicated to the resolution of a singular equation set in the half-space, with a diffusion coefficient that blows up on the boundary. More precisely, for a datum g: ℝ+3 → ℝ, our problem involves seeking u: ℝ+3 → ℝ as a formal solution to

We give existence and uniqueness results of weak and strong solutions in suitable weighted spaces, where the weight depends on x3.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2012

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