Boundary value problems for degenerate elliptic equations and systems

Pascal Auscher (1) , Andreas Rosén (2) , David Rule (3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 Matematiska Vetenskaper
3 Matematiska institutionen

We study boundary value problems for degenerate elliptic equations and systems with square integrable boundary data. We can allow for degeneracies in the form of an $A_{2}$ weight. We obtain representations and boundary traces for solutions in appropriate classes, perturbation results for solvability and solvability in some situations. The technology of earlier works of the first two authors can be adapted to the weighted setting once the needed quadratic estimate is established and we even improve some results in the unweighted setting. The proof of this quadratic estimate does not follow from earlier results on the topic and is the core of the article.

Mots clés: weighted norm inequalities; second order elliptic equations and systems; Littlewood-Paley estimates; functional calculus; boundary value problems

Domaines: Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Pascal Auscher, Andreas Rosén, David Rule. Boundary value problems for degenerate elliptic equations and systems. Annales Scientifiques de l'École Normale Supérieure, 2015, 48 (4), pp.951 -- 1000. ⟨hal-00846285v2⟩