## 12 Citations

Existence and regularity of the solutions to degenerate elliptic equations in Carnot-Carathéodory spaces

- Mathematics
- 2020

We deal with existence and regularity for weak solutions to Dirichlet problems of the type $$\begin{aligned} \left\{ \begin{array}{ll} - \mathrm{div} (A(x)Xu) +b(x)Xu + c(x)u=f\quad \hbox {in} \;…

An Improved Compact Embedding Theorem for Degenerate Sobolev Spaces

- Mathematics
- 2019

This short note investigates the compact embedding of degenerate matrix weighted Sobolev spaces into weighted Lebesgue spaces. The Sobolev spaces explored are defined as the abstract completion of…

Matrix $$\mathcal {A}_p$$Ap Weights, Degenerate Sobolev Spaces, and Mappings of Finite Distortion

- Mathematics
- 2016

We study degenerate Sobolev spaces where the degeneracy is controlled by a matrix $$\mathcal {A}_p$$Ap weight. This class of weights was introduced by Nazarov, Treil and Volberg, and degenerate…

Green functions for weighted subelliptic p-Laplace operator constructed by Hörmander's vector fields

- Mathematics
- 2016

Matrix $A_p$ weights, degenerate Sobolev spaces, and mappings of finite distortion.

- Mathematics
- 2016

We study degenerate Sobolev spaces where the degeneracy is controlled by a matrix $A_p$ weight. This class of weights was introduced by Nazarov, Treil and Volberg, and degenerate Sobolev spaces with…

Poincaré Inequalities and Neumann Problems for the p-Laplacian

- MathematicsCanadian Mathematical Bulletin
- 2018

Abstract We prove an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a Neumann problem related to a degenerate $p$ -Laplacian. The Poincaré inequalities are…

HARNACK INEQUALITIES FOR WEIGHTED SUBELLIPTIC P-LAPLACE EQUATIONS CONSTRUCTED BY HÖRMANDER VECTOR FIELDS

- Mathematics

with w = w(x) being an Ap function. We first establish a maximum principle for weak solutions to the equation Lpu = g with the weighted Sobolev inequality and the extension of Moser iteration…

Elliptic Equations with Degenerate Weights

- Mathematics, Computer ScienceSIAM J. Math. Anal.
- 2022

New local Calderon-Zygmund estimates are obtained for elliptic equations with matrix-valued weights for linear as well as non-linear equations using a novel log-BMO condition on the weight M that assumes smallness of the logarithm of the Matrix-valued weight in BMO.

## References

SHOWING 1-10 OF 52 REFERENCES

Inequalities of Hardy–Sobolev Type in Carnot–Carathéodory Spaces

- Mathematics
- 2009

We consider various types of Hardy-Sobolev inequalities on a Carnot-Carath\'eodory space $(\Om, d)$ associated to a system of smooth vector fields $X=\{X_1, X_2,...,X_m\}$ on $\RR^n$ satisfying the…

Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients

- Mathematics
- 2011

Abstract. We derive local boundedness estimates for weak solutions of a large class of secondorder quasilinear equations. The structural assumptions imposed on an equation in the class allowvanishing…

WEIGHTED POINCARE AND SOBOLEV INEQUALITIES AND ESTIMATES FOR WEIGHTED PEANO MAXIMAL FUNCTIONS

- Mathematics
- 1985

1. Introduction. In this paper, we derive local Poincare and Sobolev inequalities involving two weight functions. The estimates we obtain include those proved by Fabes, Kenig and Serapioni in [8] for…

Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)

- Mathematics
- 2009

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis.…

Mappings of finite distortion: Monotonicity and continuity

- Mathematics
- 2001

We study mappings f = ( f1, ..., fn) : Ω → Rn in the Sobolev space W loc (Ω,R n), where Ω is a connected, open subset of Rn with n ≥ 2. Thus, for almost every x ∈ Ω, we can speak of the linear…

Estimates of BMO type for singular integrals on spaces of homogeneous type and applications to hypoelliptic PDEs

- Mathematics
- 2005

Let us consider the class of "nonvariational uniformly hypoelliptic operators": Lu ≡ q � i,j=1 aij (x) XiXju where: X1 ,X 2 ,...,X q is a system of Hormander vector fields in R n ( n>q ), {aij} is a…

Degenerate Sobolev spaces and regularity of subelliptic equations

- Mathematics
- 2009

We develop a notion of degenerate Sobolev spaces naturally associated with nonnegative quadratic forms that arise from a large class of linear subelliptic equations with rough coefficients. These…

Sobolev mappings with integrable dilatations

- Mathematics
- 1993

We show that each quasi-light mapping f in the Sobolev space W1n(Ω, Rn) satisfying ¦Df(x)¦n ≦K(x, f)J(x, f) for almost every x and for some KεLr(Ω), r>n-1, is open and discrete. The assumption that f…

Nonlinear Potential Theory of Degenerate Elliptic Equations

- Mathematics
- 1993

Introduction. 1: Weighted Sobolev spaces. 2: Capacity. 3: Supersolutions and the obstacle problem. 4: Refined Sobolev spaces. 5: Variational integrals. 6: A-harmonic functions. 7: A superharmonic…