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

Donatella Danielli; Nicola Garofalo; Sandro Salsa

doi:10.1512/iumj.2003.52.2088

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 journal › Article › peer-review

17 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 Γ^1,1. This result constitutes the sub-elliptic counterpart of the classical C^1,1 regularity for Laplace equation. We also prove non-degeneracy properties of the solution and of its free boundary.

Original language	English (US)
Pages (from-to)	361-398
Number of pages	38
Journal	Indiana University Mathematics Journal
Volume	52
Issue number	2
DOIs	https://doi.org/10.1512/iumj.2003.52.2088
State	Published - 2003
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.1512/iumj.2003.52.2088

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AU - Salsa, Sandro

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AB - 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.

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KW - Obstacle problem

KW - Sub-elliptic equations

KW - Theorems of Rademacher-Stepanov type

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

Abstract

Keywords

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