Eero Ruosteenoja

activity

20142021

collaborators

8 papers

math.AP2021

Game-theoretic approach to Hölder regularity for PDEs involving eigenvalues of the Hessian

Pablo Blanc, Jeongmin Han, Mikko Parviainen +1

We prove a local Hölder estimate with an exponent $0 < δ < \frac{1}{2}$ for solutions of the dynamic programming principle $$u^\varepsilon (x) =\sum_{j=1}^n α_j\inf_{\dim(S)=j}\sup_{\subs…

math.AP2019

Gradient regularity for a singular parabolic equation in non-divergence form

Amal Attouchi, Eero Ruosteenoja

In this paper we consider viscosity solutions of a class of non-homogeneous singular parabolic equations $\partial_{t} u - ∣ D u ∣^{γ} Δ_{p}^{N} u = f,$ where $- 1 < γ < 0$ , $1 < p < \infty$ , and $f$ is…

math.AP2019

A control problem related to the parabolic dominative $p$ -Laplace equation

Fredrik Arbo Høeg, Eero Ruosteenoja

We show that value functions of a certain time-dependent control problem in $Ω \times (0, T)$ , with a continuous payoff $F$ on the parabolic boundary, converge uniformly to the visco…

math.AP2018

Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities

Ángel Arroyo, Hannes Luiro, Mikko Parviainen +1

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $Ω \subset R^{n}$ . The method of the proof is based on…

math.AP2017

Remarks on regularity for $p$ -Laplacian type equations in non-divergence form

Amal Attouchi, Eero Ruosteenoja

We study a singular or degenerate equation in non-divergence form modeled by the $p$ -Laplacian, $- ∣ D u ∣^{γ} (Δ u + (p - 2) Δ_{\infty}^{N} u) = f in Ω.$ We investiga…

math.AP2016

$C^{1, α}$ regularity for the normalized $p$ -Poisson problem

Amal Attouchi, Mikko Parviainen, Eero Ruosteenoja

We consider the normalized $p$ -Poisson problem $- Δ_{p}^{N} u = f in Ω.$ The normalized $p$ -Laplacian $Δ_{p}^{N} u := ∣ D u ∣^{2 - p} Δ_{p} u$ is in non-divergence form and arise…

math.AP2015

Local regularity for time-dependent tug-of-war games with varying probabilities

Mikko Parviainen, Eero Ruosteenoja

We study local regularity properties of value functions of time-dependent tug-of-war games. For games with constant probabilities we get local Lipschitz continuity. For more genera…

math.AP2014

Local regularity results for value functions of tug-of-war with noise and running payoff