Arttu Karppinen

activity

20192023

most citedThe weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth

41 citations · 42 across the 8 of their papers we have counts for

collaborators

9 papers

math.AP2023

Local second order regularity of solutions to elliptic Orlicz-Laplace equation

Arttu Karppinen, Saara Sarsa

We consider Orlicz--Laplace equation $- d i v (\frac{φ ^{'} ( ∣\nabla u ∣ )}{∣\nabla u ∣} \nabla u) = f$ where $φ$ is an Orlicz function and either $f = 0$ or $f \in L^{\infty}$ . We prove local second…

math.AP2023★ 1 cited

A direct proof of existence of weak solutions to fully anisotropic and inhomogeneous elliptic problems

Iwona Chlebicka, Arttu Karppinen, Ying Li

We provide a direct proof of existence and uniqueness of weak solutions to a broad family of strongly nonlinear elliptic equations with lower order terms. The leading part of the o…

math.AP2022

Stability of solutions to obstacle problems with generalized Orlicz growth

Petteri Harjulehto, Arttu Karppinen

We consider nonlinear equations having generalized Orlicz growth (also known as Musielak--Orlicz growth). We prove that if differential operators $A_{i}$ converge locally u…

math.FA2021

Fractional operators and their commutators on generalized Orlicz spaces

Arttu Karppinen

In this paper we examine boundedness of fractional maximal operator. The main focus is on commutators and maximal commutators on generalized Orlicz spaces for fractional maximal fu…

math.FA2021

Sharp growth conditions for boundedness of maximal function in generalized Orlicz spaces

Petteri Harjulehto, Arttu Karppinen

We study sharp growth conditions for the boundedness of the Hardy-Littlewood maximal function in the generalized Orlicz spaces. We assume that the generalized Orlicz function $ϕ(x,…

math.AP2020

Hölder continuity of the minimizer of an obstacle problem with generalized Orlicz growth

Arttu Karppinen, Mikyoung Lee

We prove local $C^{0, α}$ - and $C^{1, α}$ -regularity for the local solution to an obstacle problem with non-standard growth. These results cover as special cases standard, variable e…

math.AP2020★ 41 cited

The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth

Allami Benyaiche, Petteri Harjulehto, Peter Hästö +1

We study unbounded weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak--Orlicz) growth. We show that they satisfy the weak Harnack ineq…

math.AP2020

Removable sets in elliptic equations with Musielak-Orlicz growth

Iwona Chlebicka, Arttu Karppinen

We characterize, in the terms of intrinsic Hausdorff measures, the size of~removable sets for Hölder continuous solutions to elliptic equations with Musielak-Orlicz growth. In the…

math.AP2019

Global continuity and higher integrability of a minimizer of an obstacle problem under generalized Orlicz growth conditions

Arttu Karppinen

We prove continuity up to the boundary of the minimizer of an obstacle problem and higher integrability of its gradient under generalized Orlicz growth. The result recovers similar…