Demonstrates local Lipschitz regularity in weak solutions of a non-homogeneous q-Laplace equation, indicating a new understanding of solution stability.
In the Heisenberg group Hn and for exponents 2≤q≤4, the local Lipschitz (C0,1) regularity is demonstrated for weak solutions to a non-homogeneous highly degenerate q-Laplace equation of the form −∑i=12nXiλi(Xu)Xiu=g(x), where λi(z)=(zi2+zi+n2)q−22 for i=1,…,n and λi(z)=(zi2+zi−n2)q−22 for i=n+1,…,2n. Our approach draws heavily on the work of X. Zhong. However, owing to technical limitations, the regularity of weak solutions for 1<q<2 and 4<q<∞ remains unclear.
No takes yet. Share an insight, caveat, or question.
Wang et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: