English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper, we investigate the boundary behavior of solutions ofdivergence-form operators with an elliptic symmetric part and a $BMO$anti-symmetric part. Our results will hold in non-tangentially accessible (NTA)domains; these general domains were introduced by Jerison and Kenig and includethe class of Lipschitz domains. We establish the H\"older continuity of thesolutions at the boundary, existence of elliptic measures $\omega_L$ associatedto such operators, and the well-posedness of the continuous Dirichlet problemas well as the $L^p(d\omega)$ Dirichlet problem in NTA domains. The equivalencein the $L^p$ norm of the square function and the non-tangential maximalfunction under certain conditions remains valid. When specialized to Lipschitzdomains, it is then possible to extend, to these operators, various criteriafor determining mutual absolute continuity of elliptic measure with surfacemeasure.

Boundary behavior of solutions of elliptic operators in divergence form with a BMO anti-symmetric part