arXiv subjects

Maria Stella Fanciullo

Publications and source records attributed to Maria Stella Fanciullo.

7 recordsLinked to original sources

arXiv2023

Matrix Weights and Regularity for Degenerate Elliptic Equations

We prove local boundedness, Harnack's inequality and local regularity for weak solutions of quasilinear degenerate elliptic equations in divergence form with Rough coefficients. Degeneracy is encoded by a non-negative, symmetric, measurable matrix valued function Q(x) and two suitable non-negative weight functions. We setup an axiomatic approach in terms of suitable geometric conditions and local Sobolev-Poincaré inequalities. Data integrability is close to L1 and is exploited in terms of a suitable Stummel-Kato class that in some cases is necessary for local regularity.

math.AP↗

arXiv2016

On Burenkov's extension operator preserving Sobolev-Morrey spaces on Lipschitz domains

We prove that Burenkov's Extension Operator preserves Sobolev spaces built on general Morrey spaces, including classical Morrey spaces. The analysis concerns bounded and unbounded open sets with Lipschitz boundaries in the n-dimensional Euclidean space.

math.FA↗

arXiv2015

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].

math.FA↗

arXiv2013

C^{k,α}-regularity of solutions to quasilinear equations structured on Hörmander's vector fields

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

math.AP↗

arXiv2012

Hölder regularity for non divergence form elliptic equations with discontinuous coefficients

In this note we study the global regularity in the Morrey spaces for the second derivatives for the strong solutions of non variational elliptic equations.

math.AP↗

arXiv2012

BMO estimates for nonvariational operators with discontinuous coefficients structured on Hormander's vector fields on Carnot groups

We consider a class of nonvariational linear operators formed by homogeneous left invariant Hormander's vector fields with respect to a structure of Carnot group. The bounded coefficients of the operators belong to "vanishing logarithmic mean oscillation" class with respect to the distance induced by the vector fields (in particular they can be discontinuous). We prove local estimates in "local BMO" spaces intersected with the Lebesgue spaces. Even in the uniformly elliptic case our estimates improve the known results.

math.AP↗

arXiv2010

Harnack inequality and regularity for degenerate quasilinear elliptic equations

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,α}$ local estimates for solutions of a degenerate equation in non divergence form.

math.AP↗