Dirichlet integrals and Gaffney-Friedrichs inequalities in convex domains

@inproceedings{Mitrea2001DirichletIA,
  title={Dirichlet integrals and Gaffney-Friedrichs inequalities in convex domains},
  author={Marius Mitrea},
  year={2001}
}
We study geometrical conditions guaranteeing the validity of the classical GaffneyFriedrichs estimate ‖u‖H1,2(Ω) ≤ C ( ‖du‖L2(Ω) + ‖δu‖L2(Ω) + ‖u‖L2(Ω) ) (0.1) granted that the differential form u has a vanishing tangential or normal component on ∂Ω. Our main result is that (0.1) holds provided Ω satisfies a suitable convexity assumption. In the Euclidean setting, a uniform exterior ball condition suffices. As applications, certain regularity results of PDE’s and eigenvalue inequalities in… CONTINUE READING

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