W2,p a priori estimates for nonvariational operators: the sharp maximal function technique

W2,p a priori estimates for nonvariational operators: the sharp maximal function technique

We consider a nonvariational degenerate elliptic operator, structured on a system of left invariant, 1-homogeneous, Hörmander vector fields on a Carnot group, where the coefficient matrix is symmetric, uniformly positive on a bounded domain and the coefficients are locally VMO. We discuss a new proo...

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Main Author: Marco Bramanti
Format: Article
Language:English
Published: University of Bologna 2018-12-01
Series:Bruno Pini Mathematical Analysis Seminar
Subjects:
hormander vector fields
carnot groups
nonvariational operators
l^p estimates
local sharp maximal function
Online Access:https://mathematicalanalysis.unibo.it/article/view/8939
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spelling doaj-a589c725f3d54625987b7cd2ca82d7a22020-11-24T23:59:38ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292018-12-019111910.6092/issn.2240-2829/89397780W2,p a priori estimates for nonvariational operators: the sharp maximal function techniqueMarco Bramanti0Politecnico di MilanoWe consider a nonvariational degenerate elliptic operator, structured on a system of left invariant, 1-homogeneous, Hörmander vector fields on a Carnot group, where the coefficient matrix is symmetric, uniformly positive on a bounded domain and the coefficients are locally VMO. We discuss a new proof (given in [BT] and also based on results in [BF]) of the interior estimates in Sobolev spaces, first proved in [BB-To]. The present proof extends to this context Krylov' technique, introduced in [K1], consisting in estimating the sharp maximal function of second order derivatives.https://mathematicalanalysis.unibo.it/article/view/8939hormander vector fieldscarnot groupsnonvariational operatorsl^p estimateslocal sharp maximal function
collection DOAJ
language English
format Article
sources DOAJ
author Marco Bramanti
spellingShingle Marco Bramanti
W2,p a priori estimates for nonvariational operators: the sharp maximal function technique
Bruno Pini Mathematical Analysis Seminar
hormander vector fields
carnot groups
nonvariational operators
l^p estimates
local sharp maximal function
author_facet Marco Bramanti
author_sort Marco Bramanti
title W2,p a priori estimates for nonvariational operators: the sharp maximal function technique
title_short W2,p a priori estimates for nonvariational operators: the sharp maximal function technique
title_full W2,p a priori estimates for nonvariational operators: the sharp maximal function technique
title_fullStr W2,p a priori estimates for nonvariational operators: the sharp maximal function technique
title_full_unstemmed W2,p a priori estimates for nonvariational operators: the sharp maximal function technique
title_sort w2,p a priori estimates for nonvariational operators: the sharp maximal function technique
publisher University of Bologna
series Bruno Pini Mathematical Analysis Seminar
issn 2240-2829
publishDate 2018-12-01
description We consider a nonvariational degenerate elliptic operator, structured on a system of left invariant, 1-homogeneous, Hörmander vector fields on a Carnot group, where the coefficient matrix is symmetric, uniformly positive on a bounded domain and the coefficients are locally VMO. We discuss a new proof (given in [BT] and also based on results in [BF]) of the interior estimates in Sobolev spaces, first proved in [BB-To]. The present proof extends to this context Krylov' technique, introduced in [K1], consisting in estimating the sharp maximal function of second order derivatives.
topic hormander vector fields
carnot groups
nonvariational operators
l^p estimates
local sharp maximal function
url https://mathematicalanalysis.unibo.it/article/view/8939
work_keys_str_mv AT marcobramanti w2paprioriestimatesfornonvariationaloperatorsthesharpmaximalfunctiontechnique
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