Double ball property: an overview and the case of step two Carnot groups
We investigate the notion of the so-called Double Ball Property, which concerns the nonnegative sub-solutions of some differential operators. Thanks to the axiomatic approach developed in [6], this is an important tool in order to solve the Krylov-Safonov's Harnack inequality problem for this k...
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2012-12-01
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doaj-ccb968e80c524cacbefa82ce1d8a06f72020-11-24T22:19:03ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292012-12-013133473176Double ball property: an overview and the case of step two Carnot groupsGiulio Tralli0Università di BolognaWe investigate the notion of the so-called Double Ball Property, which concerns the nonnegative sub-solutions of some differential operators. Thanks to the axiomatic approach developed in [6], this is an important tool in order to solve the Krylov-Safonov's Harnack inequality problem for this kind of operators. In particular, we are interested in linear second order horizontally-elliptic operators in non-divergence formand with measurable coefficients. In the setting of homogeneous Carnot groups, we would like to stress the relation between the Double Ball Property and a kind of solvability of the Dirichlet problem for the operator in the exterior of some homogeneous balls. We present a recent result obtained in [15], where the double ball property has been proved in a generic Carnot group of step two.http://mathematicalanalysis.unibo.it/article/view/3417Degenerate-elliptic equationsinvariant Harnack inequalityhomogeneous Carnot groups. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Giulio Tralli |
spellingShingle |
Giulio Tralli Double ball property: an overview and the case of step two Carnot groups Bruno Pini Mathematical Analysis Seminar Degenerate-elliptic equations invariant Harnack inequality homogeneous Carnot groups. |
author_facet |
Giulio Tralli |
author_sort |
Giulio Tralli |
title |
Double ball property: an overview and the case of step two Carnot groups |
title_short |
Double ball property: an overview and the case of step two Carnot groups |
title_full |
Double ball property: an overview and the case of step two Carnot groups |
title_fullStr |
Double ball property: an overview and the case of step two Carnot groups |
title_full_unstemmed |
Double ball property: an overview and the case of step two Carnot groups |
title_sort |
double ball property: an overview and the case of step two carnot groups |
publisher |
University of Bologna |
series |
Bruno Pini Mathematical Analysis Seminar |
issn |
2240-2829 |
publishDate |
2012-12-01 |
description |
We investigate the notion of the so-called Double Ball Property, which concerns the nonnegative sub-solutions of some differential operators. Thanks to the axiomatic approach developed in [6], this is an important tool in order to solve the Krylov-Safonov's Harnack inequality problem for this kind of operators. In particular, we are interested in linear second order horizontally-elliptic operators in non-divergence formand with measurable coefficients. In the setting of homogeneous Carnot groups, we would like to stress the relation between the Double Ball Property and a kind of solvability of the Dirichlet problem for the operator in the exterior of some homogeneous balls. We present a recent result obtained in [15], where the double ball property has been proved in a generic Carnot group of step two. |
topic |
Degenerate-elliptic equations invariant Harnack inequality homogeneous Carnot groups. |
url |
http://mathematicalanalysis.unibo.it/article/view/3417 |
work_keys_str_mv |
AT giuliotralli doubleballpropertyanoverviewandthecaseofsteptwocarnotgroups |
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