Open AccessVariational inequalities with lack of ellipticity. Part I: Optimal interior regularity and non-degeneracy of the free boundary
Author(s) -
Donatella Danielli,
Nicola Garofalo,
Sandro Salsa
Publication year - 2003
Publication title -
indiana university mathematics journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.317
H-Index - 69
eISSN - 1943-5258
pISSN - 0022-2518
DOI - 10.1512/iumj.2003.52.2088
Subject(s) - mathematics , boundary (topology) , degeneracy (biology) , isotropy , mathematical analysis , class (philosophy) , obstacle problem , free boundary problem , boundary value problem , obstacle , carnot cycle , laplace's equation , pure mathematics , physics , bioinformatics , biology , quantum mechanics , artificial intelligence , computer science , political science , law , thermodynamics
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 reg- ularity of the solution to the obstacle problem in terms of the Folland-Stein non-isotropic class— 1;1. This result constitutes the sub-elliptic counterpart of the classicalC1;1 regularity for Laplace equation. We also prove non-degeneracy properties of the solu- tion and of its free boundary.
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