Calculus of Variations and Geometric Measure Theory

Two Seminars by N.Shanmugalingam and G.P.Leonardi

created by magnani on 05 May 2007

16 may 2007

Abstract.

ore 15:00-AULA MAGNA del Dipartimento di Matematica

Nages Shanmugalingam (Cincinnati University)

``Boundary Harnack Principle for $p$-harmonic functions in smooth Euclidean domains''

ABSTRACT. The boundary Harnack principle dictates that every harmonic function vanishing on a segment of the boundary must decay at the same rate. We will discuss the techniques used to prove this principle for smooth Euclidean domains. While now the work of John Lewis and Kaj Nyström have verified that this principle holds for more general Euclidean Lipschitz domains, their technique is not so readily available in more general metric measure spaces such as polarizable Carnot groups.

ore 16:15-AULA MAGNA del Dipartimento di Matematica

Gian Paolo Leonardi (Modena University)

``Regularity of abnormal geodesics in sub-Riemannian geometry''

ABSTRACT. The existence of sub-Riemannian geodesics of abnormal type (i.e. singular in the sense of Pontryagin Maximum Principle) has been established by R.Montgomery in 1994. The regularity of such curves is still unknown for general sub-Riemannian manifolds. In this talk, a regularity theorem concerning the elimination of corner-like singularities for length minimizing curves will be presented, as well as some corollaries. This theorem holds for a large class of equiregular sub-Riemannian manifolds and is based on a new iterative construction, aimed to finely control the end-point of an abnormal geodesic via small perturbations."