C^{k,\alpha}-regularity of solutions to quasilinear equations structured on H\"ormander's vector fields

For a linear nonvariational operator structured on smooth H\"ormander's vector fields, with H\"older continuous coefficients, we prove a regularity result in the spaces of H\"older functions. We deduce an analogous regularity result for nonvariational degenerate quasilinear equations

Partial Hölder continuity for second order non linear non variational parabolic systems with controlled growth

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The local sharp maximal function and BMO on locally homogeneous spaces

We prove a local version of Fefferman-Stein inequality for the local sharp maximal function, and a local version of John-Nirenberg inequality for locally BMO functions, in the framework of locally homogeneous spaces, in the sense of Bramanti-Zhu [Manuscripta Math. 138 (2012), no. 3-4, 477-528]

Hölder continuity for second order non variational parabolic systems

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L^{2,λ} regularity for second order non linear non variational elliptic systems

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The local sharp maximal function and BMO on locally homogeneous spaces

We prove a local version of Fefferman-Stein inequality for the local sharp maximal function, and a local version of John-Nirenberg inequality for locally BMO functions, in the framework of locally homogeneous spaces, in the sense of Bramanti-Zhu [Manuscripta Math. 138 (2012), no. 3-4, 477-528]

Wloc2,p estimates for Cordes nonlinear operators in the Heisenberg group

Abstract Our aim is to estimate the second order horizontal derivatives of the solutions for a nondivergence form subelliptic equation a ( x , u , X u , X 2 u ) = f ( x )