We adapt Levi's parametrix method to construct a local fundamental solutions for operators of the form sum_i=1^m X_i^2, where X_1,ldots, X_m are H"ormander vector fields of step 2 having non-smooth coefficients. We also provide estimates of the fundamental solution and of its derivatives.
Fundamental solutions for sum of squares of vector fields operators with C^1,α coefficients / Manfredini, M.. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - 24:(2012), pp. 973-1011. [10.1515/FORM.2011.093]
Fundamental solutions for sum of squares of vector fields operators with C^1,α coefficients
M. Manfredini
2012
Abstract
We adapt Levi's parametrix method to construct a local fundamental solutions for operators of the form sum_i=1^m X_i^2, where X_1,ldots, X_m are H"ormander vector fields of step 2 having non-smooth coefficients. We also provide estimates of the fundamental solution and of its derivatives.
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