Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

$H$-convergence for equations depending on monotone operators in Carnot groups

Alberto Maione

Abstract

Let $Ω$ be an open and bounded subset of a Carnot Group $\mathbb{G}$ and $2\leq p<\infty$. In this paper we present some results related to the convergence of solutions of Dirichlet problems for sequences of monotone operators. The aim of this paper is to give a generalization of well-known results of Tartar, De Arcangelis-Serra Cassano and Baldi-Franchi-Tchou-Tesi in more general frameworks.

$H$-convergence for equations depending on monotone operators in Carnot groups

Abstract

Let be an open and bounded subset of a Carnot Group and . In this paper we present some results related to the convergence of solutions of Dirichlet problems for sequences of monotone operators. The aim of this paper is to give a generalization of well-known results of Tartar, De Arcangelis-Serra Cassano and Baldi-Franchi-Tchou-Tesi in more general frameworks.

Paper Structure

This paper contains 7 sections, 8 theorems, 60 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Carnot groups
  4. The functional setting
  5. Monotone operators
  6. Existence results for equations driven by monotone operators
  7. H-convergence and Div-curl lemma

Key Result

Theorem 1.2

Let $\Omega\subset\mathbb{G}$ be open, connected and bounded, $2\leq p<\infty$, $\alpha\leq\beta$ positive constants and let $(A^n)_n\subset\mathcal{M}(\alpha,\beta;\Omega)$. Then, up to subsequences, there exists $A^{eff}\in\mathcal{M}(\alpha,\beta;\Omega)$ such that

Theorems & Definitions (23)

  • Definition 1.1
  • Theorem 1.2
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Proposition 2.4
  • Definition 2.5
  • Remark 2.6
  • Theorem 2.7
  • Proposition 3.1
  • ...and 13 more