Donatella Danielli

An embedding theorem and the harnack inequality for nonlinear subelliptic equations

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CAPACITARY ESTIMATES AND THE LOCAL BEHAVIOR OF SOLUTIONS OF NONLINEAR SUBELLIPTIC EQUATIONS

We establish sharp capacitary estimates for Carnot-Carathéodory rings associated to a system of vector fields of Hörmander type. Such estimates are instrumental to the study of the local behavior of singular solutions of a wide class of nonlinear subelliptic equations. One of the main results is a generalization of fundamental estimates obtained independently by Sanchez-Calle and Nagel, Stein and Wainger.

Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces

Introduction Carnot groups The characteristic set

A Notable Family of Entire Intrinsic Minimal Graphs in the Heisenberg Group which are not Perimeter Minimizing

X

A partial solution of the isoperimetric problem for the Heisenberg group

-variation,

Subelliptic mollifiers and a basic pointwise estimate of Poincaré type

X

A Fefferman-Phong Type Inequality and Applications to Quasilinear Subelliptic Equations

-perimeter and surface measure Geometric estimates from above on CC balls for the perimeter measure Geometric estimates from below on CC balls for the perimeter measure Fine differentiability properties of Sobolev functions Embedding a Sobolev space into a Besov space with respect to an upper Ahlfors measure The extension theorem for a Besov space with respect to a lower Ahlfors measure Traces on the boundary of

Optimal Regularity and the Free Boundaryin the Parabolic Signorini Problem

(\epsilon,\delta)

On the best possible character of the

domains The embedding of

L^Q

B^p_\beta(\Omega,d\mu)