In this paper we study global Gevrey/analytic hypoellipticity of the anisotropic twisted Laplacian L(p,q), depending on the powers p_j , q_j , 1 ≤ j ≤ n, which determine the anisotropy. It turns out that when p_j = q_j = 1 for all j (the case of the “classical” twisted Laplacian) then the anisotropic twisted Laplacian is globally analytic hypoelliptic, whereas when for at least one j either p_j > 1 or q_j > 1, the operator L(p,q) is globally Gevrey σ,τ hypoelliptic, for suitable multi-indices σ and τ.
Global Gevrey hypoellipticity for twisted Laplacians / Wei Xi.Li; Alberto Parmeggiani. - In: JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS. - ISSN 1662-9981. - STAMPA. - 4:3(2013), pp. 279-296. [10.1007/s11868-013-0073-1]
Global Gevrey hypoellipticity for twisted Laplacians
LI, WEIXI;PARMEGGIANI, ALBERTO
2013
Abstract
In this paper we study global Gevrey/analytic hypoellipticity of the anisotropic twisted Laplacian L(p,q), depending on the powers p_j , q_j , 1 ≤ j ≤ n, which determine the anisotropy. It turns out that when p_j = q_j = 1 for all j (the case of the “classical” twisted Laplacian) then the anisotropic twisted Laplacian is globally analytic hypoelliptic, whereas when for at least one j either p_j > 1 or q_j > 1, the operator L(p,q) is globally Gevrey σ,τ hypoelliptic, for suitable multi-indices σ and τ.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
