arXiv subjects
Publications and source records attributed to Tero Kilpeläinen.
A set in $\mathbb{R}^n$ is median porous if the logarithm of its distance function has bounded mean oscillation. We show that this property is preserved under quasiconformal mappings. In particular, median porosity is quasiconformally invariant. We also show that the stronger notion of weak porosity, by contrast, is not quasiconformally invariant.
This is a survey on problems involving equations $-\operatorname{div}{\Cal A}(x,\nabla u)=μ$, where $μ$ is a Radon measure and ${\Cal A}:\bold {R}^n\times\bold R^n\to \bold R^n$ verifies Leray-Lions type conditions. We shall discuss a potential theoretic approach when the measure is nonnegative. Existence and uniqueness, and different concepts of solutions are discussed for general signed measures.