Eigenvalue inequalities for the dirichlet problem on spheres and the growth of subharmonic functions

Friedland, Shmuel; Hayman, W. K.

doi:10.1007/bf02568147

Cited by 104 publications

(94 citation statements)

References 4 publications

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“…From this [FH,Thm. 2] deduce that for fixed s, γ is a monotone decreasing function in N (the space dimension), and that the limit exists as N tends to infinity…”

Section: The Monotonicity Formulamentioning

confidence: 91%

Regularity of a Free Boundary with Application to the Pompeiu Problem

Caffarelli¹,

Karp²,

Shahgholian³

2000

The Annals of Mathematics

104

124

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In the unit ball B(0, 1), let u and Ω (a domain in R N ) solve the following overdetermined problem:where χ Ω denotes the characteristic function, and the equation is satisfied in the sense of distributions.If the complement of Ω does not develop cusp singularities at the origin then we prove ∂Ω is analytic in some small neighborhood of the origin. The result can be modified to yield for more general divergence form operators. As an application of this, then, we obtain the regularity of the boundary of a domain without the Pompeiu property, provided its complement has no cusp singularities.

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“…From this [FH,Thm. 2] deduce that for fixed s, γ is a monotone decreasing function in N (the space dimension), and that the limit exists as N tends to infinity…”

Section: The Monotonicity Formulamentioning

confidence: 91%

Regularity of a Free Boundary with Application to the Pompeiu Problem

Caffarelli¹,

Karp²,

Shahgholian³

2000

The Annals of Mathematics

104

124

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“…Let 0 < 2ρ < r 0 < |p|. A corollary of a result of Huber [13], as noted by Friedland and Hayman (see p.137 of [6]), tells us that…”

Section: Proofs Of Theorem 1 and Corollarymentioning

confidence: 92%

Stationary Boundary Points for a Laplacian Growth Problem in Higher Dimensions

Gardiner

Sjödin

2014

Arch Rational Mech Anal

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It is known that corners of interior angle less than π/2 in the boundary of a plane domain are initially stationary for Hele Shaw flow arising from an arbitrary injection point inside the domain. This paper establishes the corresponding result for Laplacian growth of domains in higher dimensions. The problem is treated in terms of evolving families of quadrature domains for subharmonic functions.

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“…In particular, Sperner [22] (see also Friedland and Hayman [10]) proved the Faber-Krahn analog (2.14)…”

Section: Spherical Case: First Nonzero Eigenvaluesmentioning

confidence: 94%