Precedenti risultati riguardanti il principio di massimo generalizzato e la valutazione del primo autovalore per operatori uniformemente ellittici di tipo variazionale vengono estesi agli operatori subellittici di tipo Heisenberg non simmetrici e a coefficienti discontinui.

The problems of Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators are studied by several authors (see [1]–[5]). In this paper we obtain the Gevrey hypoellipticity for a degenerated quasi-elliptic operator in ${ℝ}^2$, without any restriction on the characteristic polyhedron.

We consider a class of possibly degenerate second order elliptic operators on ℝⁿ. This class includes hypoelliptic Ornstein-Uhlenbeck type operators having an additional first order term with unbounded coefficients. We establish global Schauder estimates in Hölder spaces both for elliptic equations and for parabolic Cauchy problems involving . The Hölder spaces in question are defined with respect to a possibly non-Euclidean metric related to the operator . Schauder estimates are deduced by sharp...

Let $X=(X_1,X_2,\cdots ,X_q)$ be a system of vector fields satisfying the Hörmander condition. We prove $L_X^{2,\lambda }$ local regularity for the gradient $Xu$ of a solution of the following strongly elliptic system $$-X_{\alpha }^{*}\left(a_{ij}^{\alpha \beta }\left(x\right)X_{\beta }{u}^j\right)=g_i-X_{\alpha }^{*}{f}_i^{\alpha }\left(x\right)\forall i=1,2,\cdots ,N,$$ where $a_{ij}^{\alpha \beta }\left(x\right)$ are bounded functions and belong to Vanishing Mean Oscillation space.