A compact support principle for a class of elliptic differential inequalities

Yang, Haitao

doi:10.1016/j.na.2004.05.002

Cited by 7 publications

(2 citation statements)

References 18 publications

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“…Unlike that on (L) and (SL), the literature on (CSP) is not so extensive. 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.…”

Section: The Compact Support Principle (Csp)mentioning

confidence: 99%

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

Bianchini,

Mari,

Pucci

et al. 2018

Preprint

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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.

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Section: The Compact Support Principle (Csp)mentioning

confidence: 99%

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

Bianchini,

Mari,

Pucci

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…The subject has a long history initiated with the seminal paper of Redheffer [1]; the first modern paper dealing with the Compact Support Principle on Euclidean spaces is due to Pucci, Serrin and Zou [2]. Later on, this subject has intensively been studied by several authors (see, for instance, [3][4][5], the monograph [6] and the references therein).…”

Section: Introductionmentioning

confidence: 99%