Coercivity for elliptic operators and positivity of solutions on Lipschitz domains

We show that usual second order operators in divergence form satisfy coercivity on Lipschitz domains if they are either complemented with homogeneous Dirichlet boundary conditions on a set of non-zero boundary measure or if a suitable Robin boundary condition is posed. Moreover, we prove the positiv...

Full description

Saved in:
Bibliographic Details
Published in:Archiv der Mathematik 2010-11, Vol.95 (5), p.457-468
Main Authors: Haller-Dintelmann, Robert, Rehberg, Joachim
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We show that usual second order operators in divergence form satisfy coercivity on Lipschitz domains if they are either complemented with homogeneous Dirichlet boundary conditions on a set of non-zero boundary measure or if a suitable Robin boundary condition is posed. Moreover, we prove the positivity of solutions in a general, abstract setting, provided that the right hand side is a positive functional. Finally, positive elements from W −1,2 are identified as positive measures.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-010-0184-3