Regularity of solutions to degenerate $p$-Laplacian equations

@article{CruzUribe2011RegularityOS,
  title={Regularity of solutions to degenerate \$p\$-Laplacian equations},
  author={David Cruz-Uribe and Kabe Moen and Virginia Naibo},
  journal={arXiv: Analysis of PDEs},
  year={2011}
}
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12 Citations
Highly Influential Citations
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12 Citations

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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…
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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…
A global regularity result for some degenerate elliptic systems
Elliptic Equations with Degenerate Weights
TLDR
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References

SHOWING 1-10 OF 52 REFERENCES
Inequalities of Hardy–Sobolev Type in Carnot–Carathéodory Spaces
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…
Elliptic Partial Differential Equations of Second Order
We study in this chapter a class of partial differential equations that generalize and are to a large extent represented by Laplace’s equation. These are the elliptic partial differential equations…
On the continuity of solutions to degenerate elliptic equations
Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients
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
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)
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
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
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
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
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…
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