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

Authors

  • Marco Bramanti Politecnico di Milano

DOI:

https://doi.org/10.6092/issn.2240-2829/8939

Keywords:

Hormander vector fields, Carnot groups, Nonvariational operators, L^p estimates, Local sharp maximal function

Abstract

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.

 

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Published

2018-12-31

How to Cite

Bramanti, M. (2018). W2,p a priori estimates for nonvariational operators: the sharp maximal function technique. Bruno Pini Mathematical Analysis Seminar, 9(1), 1–19. https://doi.org/10.6092/issn.2240-2829/8939

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Section

Articles