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Notes on Overdetermined Singular Problems

Francesco Esposito, Berardino Sciunzi, Nicola Soave

Abstract

We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.

Notes on Overdetermined Singular Problems

Abstract

We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
Paper Structure (3 sections, 6 theorems, 46 equations)

This paper contains 3 sections, 6 theorems, 46 equations.

Table of Contents

  1. Introduction
  2. Notations and preliminary results
  3. Proof of symmetry and classification results

Key Result

Theorem 1.1

Let $\Omega \subset {\mathbb{R}}^n$ be a bounded domain of class $\mathcal{C}^2$ with $n \geq 2$. Let $u \in C^2(\overline{\Omega} \setminus \{0\})$ be a solution to problem with a non-removable singularity at $0$Here we mean that the solution $u$ does not admit a smooth extension all over the domai

Theorems & Definitions (9)

  • Theorem 1.1
  • Corollary 1.2
  • Lemma 2.1: Lemma 3.1, EFS
  • Lemma 2.2: Lemma 3.2, EFS
  • Lemma 2.3: Lemma 1, serrin
  • proof : Proof of Theorem \ref{['thm:main']}
  • Proposition 3.1
  • proof
  • proof : Proof of Corollary \ref{['cor:class']}