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Corrigendum to "Spectral optimization for weighted anisotropic problems with Robin conditions" [J. Differ. Equ. 378, 303--338, 2024]

B. Pellacci, G. Pisante, D. Schiera

Abstract

The goal of this note is to fill a gap in the proof of the first two items of Theorem 5.1 in [4], which relies on Polya type inequalities and the characterization of the equality cases for monotone rearrangements given in Propositions 4.1 and 4.2 of [4], whose statements and proofs require some adjustments.

Corrigendum to "Spectral optimization for weighted anisotropic problems with Robin conditions" [J. Differ. Equ. 378, 303--338, 2024]

Abstract

The goal of this note is to fill a gap in the proof of the first two items of Theorem 5.1 in [4], which relies on Polya type inequalities and the characterization of the equality cases for monotone rearrangements given in Propositions 4.1 and 4.2 of [4], whose statements and proofs require some adjustments.

Paper Structure

This paper contains 3 theorems, 27 equations.

Key Result

Proposition 1

Let $u \in W^{1,p}(0, 1)$. If $u(0) \geq u(1)$ then where we have defined Otherwise, if $u(0) \leq u(1)$ then where we have defined

Theorems & Definitions (8)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • proof : Proof of conclusion $1$
  • proof : Proof of conclusion $2$