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

Marco Bramanti

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.

 


Keywords


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

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DOI: 10.6092/issn.2240-2829/8939

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Copyright (c) 2018 Marco Bramanti

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