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A Rellich type estimate for a subelliptic Helmholtz equation with mixed homogeneities

Agnid Banerjee, Nicola Garofalo

Abstract

We establish an optimal asymptotic on rings for a subelliptic Helmholtz equation with mixed homogeneities.

A Rellich type estimate for a subelliptic Helmholtz equation with mixed homogeneities

Abstract

We establish an optimal asymptotic on rings for a subelliptic Helmholtz equation with mixed homogeneities.
Paper Structure (4 sections, 11 theorems, 85 equations)

This paper contains 4 sections, 11 theorems, 85 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Background results
  4. Proof of Theorem \ref{['sharprel']}

Key Result

Theorem 1.1

Let $Q_\alpha\ge 3$ and let $f\not\equiv 0$ be a solution to for some $\kappa>0$. There exists $R_1>R_0$ sufficiently large, and a constant $M = M(m,k,f)>0$ such that for $R>R_1$ one has

Theorems & Definitions (21)

  • Theorem 1.1
  • Theorem 1.2
  • Remark 1.3
  • Lemma 2.1
  • Lemma 2.2
  • proof
  • Proposition 2.3
  • proof
  • Lemma 3.1
  • proof
  • ...and 11 more