6 papers
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 converge locally u…
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…
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,…
Hölder continuity of the minimizer of an obstacle problem with generalized Orlicz growth
Arttu Karppinen, Mikyoung Lee
We prove local - and -regularity for the local solution to an obstacle problem with non-standard growth. These results cover as special cases standard, variable e…
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…
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…