Fundamental solutions for sum of squares of vector fields operators with C1,α coefficients

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2012 Italy Publisher:Walter de Gruyter GmbHJournal:Forum Mathematicum, volume 24 (issn: 0933-7741, eissn: 1435-5337,

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Authors: MANFREDINI, MARIA;

doi: 10.1515/form.2011.093

handle: 11380/1189340 , 11585/96503

Fundamental solutions for sum of squares of vector fields operators with C1,α coefficients

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Abstract

Consider in \(\mathbb{R}^n_x\) the sum-of-squares \(L=\sum_{j=1}^mX_j^2\), \(1\leq m\leq n\), where the locally Euclidean Lipschitz continuous vector fields \(X_j\) have the form \[ X_j=\frac{\partial}{\partial x_j}+\sum_{k=m+1}^na_{jk}(x)\frac{\partial}{\partial x_k},\,\,\,\,1\leq j\leq m, \] and satisfy the step-two condition \[ \frac{\partial}{\partial x_j}=\sum_{1\leq i

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Keywords

sub-elliptic operators, fundamental solution, Analysis on other specific Lie groups, Parametrices in context of PDEs, SUBELLIPTIC OPERATOR; FUNDAMENTAL SOLUTION; NON SMOOTH VECTYOR FIELDS, Subelliptic equations, Fundamental solutions to PDEs, Degenerate elliptic equations, Levi parametrix method

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