Let the vector fields $$X_1, \ldots , X_{6}$$ X 1 , … , X 6 form an orthonormal basis of $$\mathcal {H}$$ H , the orthogonal complement of a Cartan subalgebra (of dimension 2) in $${{\,\mathrm{SU}\,}}(3)$$ SU ( 3 ) . We prove that weak solutions u to the degenerate subelliptic p-Laplacian $$\begin{aligned} \Delta _{\mathcal {H},{p}} u(x)=\sum _{i=1}^{6} X_i^{*}\left( |\nabla _{\!{\mathcal {H}}}u|^{p-2}X_{i}u \right) =0, \end{aligned}$$ Δ H , p u ( x ) = ∑ i = 1 6 X i ∗ | ∇ H u | p - 2 X i u = 0 , have Hölder continuous horizontal derivatives $$\nabla _{\!{\mathcal {H}}}u=(X_1u, \ldots , X_{6}u)$$ ∇ H u = ( X 1 u , … , X 6 u ) for $$p\ge 2$$ p ≥ 2 . We also prove that a similar result holds for all compact connected semisimple Lie groups.
Analysis and Mathematical Physics – Springer Journals
Published: Dec 24, 2019
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.