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.
@article{8939,
title = {W2,p a priori estimates for nonvariational operators: the sharp maximal function technique},
journal = {Bruno Pini Mathematical Analysis Seminar},
year = {2018},
doi = {10.6092/issn.2240-2829/8939},
language = {EN},
url = {http://dml.mathdoc.fr/item/8939}
}
Bramanti, Marco. W2,p a priori estimates for nonvariational operators: the sharp maximal function technique. Bruno Pini Mathematical Analysis Seminar, (2018), . doi : 10.6092/issn.2240-2829/8939. http://gdmltest.u-ga.fr/item/8939/