Asymptotic paths for subsolutions of quasilinear elliptic equations.
The boundary absolute continuity of quasiconformal mappings (II).
In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B → D, where B is the unit 3-ball and D is a Jordan domain in R with boundary 2-rectifiable in the sense of geometric measure theory. Moreover, examples are constructed, for each n ≥ 3, showing that quasiconformal maps from the unit n-ball onto Jordan domains with boundary (n - 1)-rectifiable need not have absolutely continuous boundary values.
Quasiconformal mappings onto John domains.
In this paper we study quasiconformal homeomorphisms of the unit ball B = B = {x ∈ R: |x| < 1} of R onto John domains. We recall that John domains were introduced by F. John in his study of rigidity of local quasi-isometries [J]; the term John domain was coined by O. Martio and J. Sarvas seventeen years later [MS]. From the various equivalent characterizations we shall adapt the following definition based on diameter carrots, cf. [V4], [V5], [NV].
A theorem of Semmes and the boundary absolute continuity in all dimensions.
We use a recent theorem of Semmes to resolve some questions about the boundary absolute continuity of quasiconformal maps in space.
Weighted Sobolev and Poincaré Inequalities and Quasiregular Mappings of Polynomial Type.
Smooth quasiregular mappings with branching
We give an example of a -smooth quasiregular mapping in 3-space with nonempty branch set. Moreover, we show that the branch set of an arbitrary quasiregular mapping in-space has Hausdorff dimension quantitatively bounded away from . By using the second result, we establish a new, qualitatively sharp relation between smoothness and branching.
Definitions of quasiconformality.
Polar sets for supersolutions of degenerate elliptic equations.
Fine topology and quasilinear elliptic equations
It is shown that the -fine topology defined via a Wiener criterion is the coarsest topology making all supersolutions to the -Laplace equation continuous. Fine limits of quasiregular and BLD mappings are also studied.
Quasiconformal mappings with Sobolev boundary values
We consider quasiconformal mappings in the upper half space of , , whose almost everywhere defined trace in has distributional differential in . We give both geometric and analytic characterizations for this possibility, resembling the situation in the classical Hardy space . More generally, we consider certain positive functions defined on , called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems for them....
Strongly uniform domains and periodic quasiconformal maps.
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