Variational inequalities with lack of ellipticity part I: Optimal interior regularity and non-degeneracy of the free boundary

Donatella Danielli, Nicola Garofalo, Sandro Salsa

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

This paper is the first part of a program aimed at studying the regularity of sub-elliptic free boundaries. In the setting of Carnot groups we establish the optimal interior regularity of the solution to the obstacle problem in terms of the Folland-Stein non-isotropic class Γ1,1. This result constitutes the sub-elliptic counterpart of the classical C1,1 regularity for Laplace equation. We also prove non-degeneracy properties of the solution and of its free boundary.

Original languageEnglish (US)
Pages (from-to)361-398
Number of pages38
JournalIndiana University Mathematics Journal
Volume52
Issue number2
DOIs
StatePublished - 2003
Externally publishedYes

Keywords

  • Carnot groups
  • Free boundaries
  • Obstacle problem
  • Sub-elliptic equations
  • Theorems of Rademacher-Stepanov type

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Variational inequalities with lack of ellipticity part I: Optimal interior regularity and non-degeneracy of the free boundary'. Together they form a unique fingerprint.

Cite this