On the p-torsion functions of an annulus

Bueno, Hamilton; Ercole, Grey

doi:10.3233/asy-141275

Cited by 2 publications

(4 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof of part (ii) of Theorem 1.2. It is known (see, for instance, [7] and also references therein) that concentric annulus Ω 0 is calibrable, (i.e., Ω 0 itself is a Cheeger set of Ω 0 ) and hence…”

Section: Proof Of Theorem 11mentioning

confidence: 99%

On the strict monotonicity of the first eigenvalue of the 𝑝-Laplacian on annuli

Anoop

Bobkov

Sasi

2018

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Let B 1 be a ball in R N centred at the origin and B 0 be a smaller ball compactly contained in B 1 . For p ∈ (1, ∞), using the shape derivative method, we show that the first eigenvalue of the p-Laplacian in annulus B 1 \ B 0 strictly decreases as the inner ball moves towards the boundary of the outer ball. The analogous results for the limit cases as p → 1 and p → ∞ are also discussed. Using our main result, further we prove the nonradiality of the eigenfunctions associated with the points on the first nontrivial curve of the Fučik spectrum of the p-Laplacian on bounded radial domains. Mathematics Subject Classification (2010): 35J92, 35P30, 35B06, 49R05. Ω |∇u| p dx : u ∈ W 1,p 0 (Ω) \ {0} with u p = 1 .In this article we consider Ω of the formdenotes the open ball of radius r > 0 centred at z ∈ R N . Since the p-Laplacian is invariant under orthogonal transformations, it can be easily seen that λ 1 (B R 1 (x) \ B R 0 (y)) = λ 1 (B R 1 (0) \ B R 0 (se 1 ))

show abstract

Section: Proof Of Theorem 11mentioning

confidence: 99%

On the strict monotonicity of the first eigenvalue of the 𝑝-Laplacian on annuli

Anoop

Bobkov

Sasi

2018

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Therefore,

B_{0}

is concentric with

B_{1}

and

B_{R}

, and

E_{1} \subset B_{0} ∖ \bar{B_{R}}

and

E_{2} \subset B_{1} ∖ \bar{B_{0}}

. However, it is known that rings

B_{0} ∖ \bar{B_{R}}

and

B_{1} ∖ \bar{B_{0}}

are calibrable , that is, they are Cheeger sets of themselves. This implies that

E_{1} = B_{0} ∖ \bar{B_{R}}

and hence

\partial false(E_{1} E_{2} false) = \partial B_{0}

, that is,

\partial (E_{1} E_{2})

is closed.…”

Section: Applicationsmentioning

confidence: 99%

“…Let us remark that these adjustment conditions are not necessary for the problem defined in (6), since in this case the Cheeger constant of each component E i of a minimizer (E 1 , . .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the higher Cheeger problem

Bobkov

Parini

2018

J. London Math. Soc.

View full text Add to dashboard Cite

We develop the notion of higher Cheeger constants for a measurable set Ω ⊂ R N . By the kth Cheeger constant we mean the valuewhere the infimum is taken over all k-tuples of mutually disjoint subsets of Ω, and h1(Ei) is the classical Cheeger constant of Ei. We prove the existence of minimizers satisfying additional 'adjustment' conditions and study their properties. A relation between h k (Ω) and spectral minimal k-partitions of Ω associated with the first eigenvalues of the p-Laplacian under homogeneous Dirichlet boundary conditions is stated. The results are applied to determine the second Cheeger constant of radially symmetric planar domains.

show abstract

On the p-torsion functions of an annulus

Cited by 2 publications

References 8 publications

On the strict monotonicity of the first eigenvalue of the 𝑝-Laplacian on annuli

On the strict monotonicity of the first eigenvalue of the 𝑝-Laplacian on annuli

On the higher Cheeger problem

Contact Info

Product

Resources

About