Elliptic and Parabolic Equations - Abstract

Haller--Dintelmann, Robert

Coercivity for elliptic operators and positivity of solutions on Lipschitz domains

We show that usual divergence $2^textnd$ order operators satisfy coercivity on Lipschitz domains if either a homogeneous Dirichlet condition is posed 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.
This is joint work with Joachim Rehberg.