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

Autor: Marco Bramanti
Jazyk: English<br />Italian
Rok vydání: 2018
Předmět:
Zdroj: Bruno Pini Mathematical Analysis Seminar, Vol 9, Iss 1, Pp 1-19 (2018)
Druh dokumentu: article
ISSN: 2240-2829
DOI: 10.6092/issn.2240-2829/8939
Popis: 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.
Databáze: Directory of Open Access Journals
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