WIAS Preprint No. 1473, (2009)

Coercivity for elliptic operators and positivity of solutions on Lipschitz domains



Authors

  • Haller-Dintelmann, Robert
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 35B05 35J20 35R05

Keywords

  • Coercivity, mixed boundary problems, positivity of solutions

DOI

10.20347/WIAS.PREPRINT.1473

Abstract

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.

Appeared in

  • Arch. Math. (Basel), 95 (2010) pp. 457--468.

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