Page 1 Local and Global Aspects of Quasilinear Degenerate Elliptic Equations Quasilinear
Elliptic Singular Problems Laurent Véron . \º WOrld Scientific Page 2 Local and Global Aspects …

We consider the boundary value problem (P λ) u∈ H 0 1 (Ω)∩ L∞(Ω):− Δ u= λ c (x) u+ μ
(x)|∇ u| 2+ h (x), where Ω⊂ RN, N≥ 3 is a bounded domain with smooth boundary. It is …

We show that different notions of solutions to measure data problems involving p-Laplace
type operators and nonnegative source measures are locally essentially equivalent. As an …

We show that a class of divergence-form elliptic problems with quadratic growth in the
gradient and non-coercive zero order terms are solvable, under essentially optimal …

We obtain global bounds in Lorentz–Morrey spaces for gradients of solutions to a class of
quasilinear elliptic equations with low integrability data. The results are then applied to …

We study some properties of the solutions of (E)− Δ p u+|∇ u| q= 0 in a domain Ω⊂ RN,
mostly when p≥ q> p− 1. We give a universal a priori estimate of the gradient of the …

We give necessary and sufficient conditions for the existence of weak solutions to the model
equation− Δ pu= σ uq on R n, in the case 0< q< p− 1, where σ≥ 0 is an arbitrary locally …

We study local and global properties of positive solutions of− Δ u= up|∇ u| q in a domain Ω
of RN, in the range p+ q> 1, p≥ 0, 0≤ q< 2. We first prove a local Harnack inequality and …

We consider the elliptic equation-Δ⁢ u= uq⁢|∇⁡ u| p in ℝ n for any p> 2 and q> 0. We prove
a Liouville-type theorem, which asserts that any positive bounded solution is constant. The …

We consider the elliptic quasilinear equation-Δ m⁢ u= up⁢|∇⁡ u| q in ℝ N, q≥ m and p> 0,
1< m< N. Our main result is a Liouville-type property, namely, all the positive C 1 solutions in …