A Liouville theorem for $$p$$ p -harmonic functions on exterior domains

A Liouville theorem for $$p$$ p -harmonic functions on exterior domains We prove Liouville type theorems for $$p$$ p -harmonic functions on exterior domains of $${\mathbb {R}}^{d}$$ R d , where $$1<p<\infty$$ 1 < p < ∞ and $$d\ge 2$$ d ≥ 2 . We show that every positive $$p$$ p -harmonic function satisfying zero Dirichlet, Neumann or Robin boundary conditions and having zero limit as $$|x|$$ | x | tends to infinity is identically zero. In the case of zero Neumann boundary conditions, we establish that any semi-bounded $$p$$ p -harmonic function is constant if $$1<p<d$$ 1 < p < d . If $$p\ge d$$ p ≥ d , then it is either constant or it behaves asymptotically like the fundamental solution of the homogeneous $$p$$ p -Laplace equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

A Liouville theorem for $$p$$ p -harmonic functions on exterior domains

, Volume 19 (3) – Dec 10, 2014
10 pages

/lp/springer_journal/a-liouville-theorem-for-p-p-harmonic-functions-on-exterior-domains-0NQHUg2hI2
Publisher
Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-014-0316-2
Publisher site
See Article on Publisher Site

DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month Explore the DeepDyve Library Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. Organize your research It’s easy to organize your research with our built-in tools. Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

14-day Free Trial

Best Deal — 39% off

Annual Plan

• All the features of the Professional Plan, but for 39% off!
• Billed annually
• No expiration
• For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588$360/year

billed annually

14-day Free Trial