Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A comment on an $L^\frac{2n}{n+2}-L^\frac{2n}{n-2}$ Carleman inequality in relation to "the determination of an unbounded potential from Cauchy data"

Mourad Choulli, Hiroshi Takase

Abstract

The proof of \cite[Proposition 2.1]{DKS}[arXiv:1104.0232] is partially incorrect. In this short note, we provide a new proof, which requires an additional hypothesis. A modification of this new proof also corrects the proof of \cite[Proposition 2.1]{Ch}[arXiv:2310.17456], where the incorrect argument of \cite{DKS} has been repeated.

A comment on an $L^\frac{2n}{n+2}-L^\frac{2n}{n-2}$ Carleman inequality in relation to "the determination of an unbounded potential from Cauchy data"

Abstract

The proof of \cite[Proposition 2.1]{DKS}[arXiv:1104.0232] is partially incorrect. In this short note, we provide a new proof, which requires an additional hypothesis. A modification of this new proof also corrects the proof of \cite[Proposition 2.1]{Ch}[arXiv:2310.17456], where the incorrect argument of \cite{DKS} has been repeated.
Paper Structure (2 sections, 2 theorems, 66 equations)

This paper contains 2 sections, 2 theorems, 66 equations.

Table of Contents

  1. Supplementary comments
  2. Acknowledgment

Key Result

Theorem 1

For all $\tau \in \Lambda$ and $u\in C_0^\infty (M)$, we have

Theorems & Definitions (4)

  • Theorem 1
  • Lemma 1
  • proof
  • proof : Proof of Theorem \ref{['thmci']}