Liouville type results and a maximum principle for non-linear differential operators on the Heisenberg group

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:415

Article

Brandolini, Luca¹  Magliaro, Marco¹ 

[1] Univ Bergamo, Dipartimento Ingn, I-24044 Dalmine, BG, Italy

关键词: Lionville theorem;    Keller-Osserman;    Heisenberg group;    Non-linear differential inequalities;   

DOI  :  10.1016/j.jmaa.2014.01.087

来源: Elsevier

【 摘 要 】

We prove Liouville type results for non-negative solutions of the differential inequality Delta(phi)u >= f(u)l(vertical bar del(0)u vertical bar) on the Heisenberg group under a generalized Keller-Osserman condition. The operator Delta(phi)u is the phi-Laplacian defined by div(0)(vertical bar del(0)u vertical bar(-1)phi(vertical bar del(0)u vertical bar)del(0)u) and phi, f and l satisfy mild structural conditions. In particular, l is allowed to vanish at the origin. A key tool that can be of independent interest is a strong maximum principle for solutions of such differential inequality. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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