Convex rearrangement: Equality cases in the P�lya-Szeg� Inequality

Ferone, Adele; Volpicelli, Roberta

doi:10.1007/s00526-003-0256-3

Cited by 34 publications

(21 citation statements)

References 15 publications

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“…Thanks to the result of [8,9], equality is attained if and only if Ω = x + s K * , then the proof of the second part of the statement is as in Proposition 3.7.…”

Section: −mentioning

confidence: 95%

On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique

Brasco

2014

ESAIM: COCV

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“…Thanks to the result of [8,9], equality is attained if and only if Ω = x + s K * , then the proof of the second part of the statement is as in Proposition 3.7.…”

Section: −mentioning

confidence: 95%

On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique

Brasco

2014

ESAIM: COCV

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“…Note that (1.2) and (1.3) can be regarded as special instances of the Pólya-Szegö principle, concerning the monotonicity of Dirichlet type integrals under appropriate symmetrizations (see e.g. [19,20,3,21,18,16,1,22,9,14,10]). …”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Functions of bounded variation and polarization

Alberico

Ferone²,

Volpicelli

2009

Mathematische Nachrichten

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“…Moreover, the equality case is characterized in the following result, contained in and : Theorem If u is a nonnegative function in

W_{0}^{1, p} (Ω)

such that

|{| D u^{☆} | = 0} \cap {0 < u^{☆} {< ∥ u ∥}_{\infty}}| = 0,

and

\int_{Ω} H {(D u)}^{p} d x = \int_{Ω^{☆}} H {(D u^{☆})}^{p} d x,

then, up to translation,

u = u^{☆}

a.e. in Ω and

Ω = Ω^{☆}

.…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Sharp bounds for the first eigenvalue and the torsional rigidity related to some anisotropic operators

Pietra

Gavitone

2013

Mathematische Nachrichten

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In this paper we prove a sharp upper bound for the first Dirichlet eigenvalue of a class of nonlinear elliptic operators which includes the operator Δpu=∑i∂∂xi|∇u|p−2-0.16em∂u∂xi, that is the p‐Laplacian, and trueΔ̃pu=∑i∂∂xi|∂u∂xi|p−2∂u∂xi, namely the pseudo‐p‐Laplacian. Moreover we prove a stability result by means of a suitable isoperimetric deficit. Finally, we give a sharp lower bound for the anisotropic p‐torsional rigidity.

show abstract

Convex rearrangement: Equality cases in the P�lya-Szeg� Inequality

Cited by 34 publications

References 15 publications

On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique

On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique

Functions of bounded variation and polarization

Sharp bounds for the first eigenvalue and the torsional rigidity related to some anisotropic operators

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