Harmonic Measure and Some Removability Problems
نویسندگان
چکیده
We deal with some applications of Marcinkiewicz integrals to problems related to harmonic measure on the one hand, and to removability problems for Sobolev spaces and quasiconformal mappings on the other hand. Techniques of this type have been used by Carleson, Jones, Makarov, Smirnov... to address these problems, and as a general program to understand harmonic functions on complicated domains in R.
منابع مشابه
The Riesz Transform, Rectifiability, and Removability for Lipschitz Harmonic Functions
We show that, given a set E ⊂ Rn+1 with finite n-Hausdorff measure Hn, if the n-dimensional Riesz transform
متن کاملRemovability of singularities of harmonic maps into pseudo-riemannian manifolds
We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R into a pseudoRiemannian manifold which is two times continuously differentiable and harmonic everywhere outside an isolated point is actually smooth harmonic everywhere. Introduction Given n ∈ N and two nonnegat...
متن کاملRemovability of Singular Sets of Harmonic Maps
We prove that a harmonic map with small energy and monotonicity property is smooth if its singular set is rectifiable and has a finite uniform density; moreover, the monotonicity property holds if the singular set has a lower dimension or its gradient has higher integrability. This work generalizes the results in [CL][DF][LG12], which were proved under the assumptions that the singular sets are...
متن کاملOptimal Sitting, Sizing, and Operation of Batteries and Passive Filters to Mitigate Over-voltage and Harmonic Problems in Distribution Networks with High Photovoltaic Penetration
Photovoltaic systems (PVs), despite their many advantages, may have effects such as power quality issues (voltage and harmonics increase), short-circuits level increase, protection issues, and transient stability for network. Some of these effects are due to the high PV penetration, which encounters the network with the over-voltage and harmonics problems. In this paper, the location, size and ...
متن کاملRemovability of Singularities with Anisotropic Growth
Abstract. With help of suitable anisotropic Minkowski’s contents and Hausdorff measures some results are obtained concerning removability of singularities for solutions of partial differential equations with anisotropic growth in the vicinity of the singular set.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005