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

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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