arXiv subjects

Jonne Juusti

Publications and source records attributed to Jonne Juusti.

5 recordsLinked to original sources

arXiv2022

Bloch estimates in non-doubling generalized Orlicz spaces

We study minimizers of non-autonomous functionals \begin{align*} \inf_u \int_Ωφ(x,|\nabla u|) \, dx \end{align*} when $φ$ has generalized Orlicz growth. We consider the case where the upper growth rate of $φ$ is unbounded and prove the Harnack inequality for minimizers. Our technique is based on "truncating" the function $φ$ to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.

math.AP↗

arXiv2022

Extension in generalized Orlicz--Sobolev spaces

We study the existence of an extension operator $Λ\colon W^{1,φ}(Ω)\to W^{1,ψ}(\mathbb{R}^n)$. We assume that $φ\in Φ_\mathrm{w}(Ω)$ has generalized Orlicz growth, $ψ\in Φ_\mathrm{w}(\mathbb{R}^n)$ is an extension of $φ$, and that $Ω\subset\mathbb{R}^n$ is an $(ε,δ)$-domain. Special cases include the classical constant exponent case, the Orlicz case, the variable exponent case, and the double phase case.

math.FA↗

arXiv2022

Riesz spaces with generalized Orlicz growth

We consider a Riesz $ϕ$-variation for functions $f$ defined on the real line when $φ:Ω\times[0,\infty)\to[0,\infty)$ is a generalized $Φ$-function. We show that it generates a quasi-Banach space and derive an explicit formula for the modular when the function $f$ has bounded variation. The resulting $BV$-type energy has previously appeared in image restoration models. We generalize and improve previous results in the variable exponent and Orlicz cases and answer a question regarding the Riesz--Medvedev variation by Appell, Banaś and Merentes [\emph{Bounded Variation and Around}, Studies in Nonlinear Analysis and Applications, Vol. 17, De Gruyter, Berlin/Boston, 2014].

math.FA↗

arXiv2021

Fuglede's theorem in generalized Orlicz--Sobolev spaces

In this paper, we show that Orlicz--Sobolev spaces $W^{1,ϕ}(Ω)$ can be characterized with the ACL- and ACC-characterizations. ACL stands for absolutely continuous on lines and ACC for absolutely continuous on curves. Our results hold under the assumptions that $C^1(Ω)$ functions are dense in $W^{1,ϕ}(Ω)$, and $ϕ(x,β) \geq 1$ for some $β> 0$ and almost every $x \in Ω$. The results are new even in the special cases of Orlicz and double phase growth.

math.FA↗

arXiv2020

The Kellogg property under generalized growth conditions

We study minimizers of the Dirichlet phi-energy integral with generalized Orlicz growth. We prove the Kellogg property, the set of irregular points has zero capacity, and give characterizations of semiregular boundary points. The results are new ever for the special cases double phase and Orlicz growth.

math.AP↗