Counterexamples for unique continuation.
Lusin's condition (N) and mappings of the class W1, n.
Long term effects in learning mathematics in Finland--curriculum changes and calculators
On a theorem of Lindelöf
We give a quasiconformal version of the proof for the classical Lindelöf theorem: Let f map the unit disk D conformally onto the inner domain of a Jordan curve C. Then C is smooth if and only if arh f'(z) has a continuous extension to D. Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.
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.
Estimates for the energy integral of quasiregular mappings on Riemannian manifolds and isoperimetry
The rate of growth of the energy integral of a quasiregular mapping is estimated in terms of a special isoperimetric condition on . The estimate leads to new Phragmén-Lindelöf type theorems.
Linear distortion of Hausdorff dimension and Cantor's function.
Let be a mapping from a metric space X to a metric space Y, and let α be a positive real number. Write dim (E) and H(E) for the Hausdorff dimension and the s-dimensional Hausdorff measure of a set E. We give sufficient conditions that the equality dim (f(E)) = αdim (E) holds for each E ⊆ X. The problem is studied also for the Cantor ternary function G. It is shown that there is a subset M of the Cantor ternary set such that H(M) = 1, with s = log2/log3 and dim(G(E)) = (log3/log2) dim (E), for every...
On a theorem of Lindelof
We give a quasiconformal version of the proof for the classical Lindelof theorem: Let map the unit disk conformally onto the inner domain of a Jordan curve : Then is smooth if and only if arg has a continuous extension to . Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.
Potential theory of quasiminimizers.
The Sobolev capacity on metric spaces.
Local and global integrability of gradients in obstacle problems.
Removable singularities of -differential forms and quasiregular mappings.
On conformal dilatation in space.
Fuglede's theorem in variable exponent Sobolev space.
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