Global Lp -integrability of the derivative of a quasiconformal mapping

Let f be a quasiconformal mapping of an open bounded set U in Rn into Rn . Then f′ belongs to Lp(U) for some p > n provided that f satisfies (a) U is a uniform domain and fU is a John domain or (b) f is quasisymmetric and U satisfies a metric plumpness condition.

Regularity and polar sets for supersolutions of certain degenerate elliptic equations

On considere l'equation ⊇•⊇ h F(x,⊇u(x))=0. Cette equation est non lineaire et degeneree avec des coefficients mesurables. On etudie la regularite des supersolutions

Phragmén-Lindelöf's and Lindelöf's theorems

Two theorems of N. Wiener for solutions of quasilinear elliptic equations

Relatively little is known about boundary behavior of solutions of quasilinear elliptic partial differential equations as compared to that of harmonic functions. In this paper two results, which in the harmonic case are due to N. Wiener, are generalized to a nonlinear situation. Suppose that G is a bounded domain in R n. We consider functions u: G--~R which are free extremals of the variational integral

Quasiextremal distance domains and extension of quasiconformal mappings

Quasiconformal mappings and F-harmonic measure

Harmonic morphisms in nonlinear potential theory

This article concerns the following problem: given a family of partial differential operators with similar structure and given a continuous mapping f from an open set Ω in Rn into Rn, then when does f pull back the solutions of one equation in the family to solutions of another equation in that family? This problem is typical in the theory of differential equations when one wants to use a coordinate change to study solutions in a different environment.

ACL homeomorphisms and linear dilatation

We establish an integrability condition on the linear dilatation to guarantee ACL.

Elliptic equations and maps of bounded length distortion

On considere l'equation elliptique d'ordre 2: L(u)=Σ i,f=1 n ∂ 1 (a ij ∂ ju )=0 ou les coefficients a ij sont des fonctions C 1 dans un domaine D de R n