Behavior of Solutions to the Dirichlet Problem for Elliptic Systems in Convex Domains
2009 (English)In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, ISSN 0360-5302 , Vol. 34, no 1, 24-51 p.Article in journal (Refereed) Published
We consider the Dirichlet problem for strongly elliptic systems of order 2m in convex domains. Under a positivity assumption on the Poisson kernel it is proved that the weak solution has bounded derivatives up to order m provided the outward unit normal has no big jumps on the boundary. In the case of second order symmetric systems in plane convex domains the boundedness of the first derivatives is proved without the assumption on the normal.
Place, publisher, year, edition, pages
2009. Vol. 34, no 1, 24-51 p.
Convex domains, Dirichlet problem, Elliptic systems, Regularity of solutions
IdentifiersURN: urn:nbn:se:liu:diva-17516DOI: 10.1080/03605300802523479OAI: oai:DiVA.org:liu-17516DiVA: diva2:209911