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Juha Kinnunen

Publications and source records attributed to Juha Kinnunen.

41 records · Page 3Linked to original sources
arXiv2013

Parabolic comparison principle and quasiminimizers in metric measure spaces

We give several characterizations of parabolic (quasisuper)- minimizers in a metric measure space equipped with a doubling measure and supporting a Poincaré inequality. We also prove a version of comparison principle for super- and subminimizers on parabolic space-time cylinders and a uniqueness result for minimizers of a boundary value problem. We also give an example showing that the corresponding results do not hold, in general, for quasiminimizers even in the Euclidean case.

math.AP↗
arXiv2012

Local approximation of superharmonic and superparabolic functions in nonlinear potential theory

We prove that arbitrary superharmonic functions and superparabolic functions related to the $p$-Laplace and the $p$-parabolic equations are locally obtained as limits of supersolutions with desired convergence properties of the corresponding Riesz measures. As an application we show that a family of uniformly bounded supersolutions to the $p$-parabolic equation contains a subsequence that converges to a supersolution.

math.AP↗
arXiv2011

How to recognize polynomials in higher order Sobolev spaces

This paper extends characterizations of Sobolev spaces by Bourgain, Brézis, and Mironescu to the higher order case. As a byproduct, we obtain an integral condition for the Taylor remainder term, which implies that the function is a polynomial. Similar questions are also considered in the context of Whitney jets.

math.CA↗
arXiv2011

Regularity of sets with quasiminimal boundary surfaces in metric spaces

This paper studies regularity of perimiter quasiminimizing sets in metric measure spaces with a doubling measure and a Poincare inequality. The main result shows that the measure theoretic boundary of a quasiminimizing set coincides with the topological boundary. We also show that such a set has finite Minkowski content and apply the regularity theory to study rectifiability issues related to quasiminimal sets in strong A_{\infty}-weighted Euclidean case.

math.AP↗