The compact support principle for differential inequalities with gradient terms

Rigoli, Marco; Salvatori, Maura; Vignati, M.

doi:10.1016/j.na.2010.02.017

Cited by 3 publications

(3 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The subject initiated with the seminal paper by R. Redheffer [131], and received a renewed interest in the last 15 years starting from [125], see also [64,117,51] and the monograph [123]. However, all of these works consider the problem in the setting of Euclidean space, and to our knowledge just [120,132,136] analyze the role played by the geometry of the manifold. As we shall see, the link between geometry and (CSP) does not depend on the validity of a maximum principles at infinity: to explain which geometric conditions are to be expected, we first comment on the following result in [120, Thm.…”

Section: The Compact Support Principle (Csp)mentioning

confidence: 99%

“…We first describe our main ODE result, that should be compared to Lemma 4.1 in [136]. Here, we consider a different and (in some cases) weaker set of assumptions, and the proof that we present is considerably simpler.…”

Section: General Operators and No Cut-locusmentioning

confidence: 99%

“…We are ready to state our second main ODE result, to be compared to Proposition 7.8. Its delicate proof originates from the paper [121], later refined in [120], [132] and [136], and to help readability we postpone it to the end of this section. Proposition 7.19.…”

Section: General Operators and No Cut-locusmentioning

confidence: 99%

See 2 more Smart Citations

On the interplay among maximum principles, compact support principles and Keller-Osserman conditions on manifolds

Bianchini,

Mari,

Pucci

et al. 2018

Preprint

Self Cite

View full text Add to dashboard Cite

This paper is about the influence of Geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, we study classes of coercive differential inequalities of the formon domains of a manifold M , for suitable ϕ, b, f, l, with emphasis on mean curvature type operators. We investigate the validity of strong maximum principles, compact support principles and Liouville type theorems; in particular, the goal is to identify sharp thresholds, involving curvatures or volume growth of geodesic balls in M , to guarantee the above properties under appropriate Keller-Osserman type conditions, and to discuss the geometric reasons behind the existence of such thresholds. The paper also aims to give a unified view of recent results in the literature. The bridge with Geometry is realized by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau's Hessian and Laplacian principles and subsequent improvements.

show abstract