Jarkko Siltakoski

activity

20172026

most citedElliptic Harnack's inequality for a singular nonlinear parabolic equation in non-divergence form

3 citations · 5 across the 12 of their papers we have counts for

collaborators

15 papers

math.AP2026

Nonnegative Viscosity and Weak Solutions to Trudinger's Parabolic Equation

Peter Lindqvist, Mikko Parviainen, Jarkko Siltakoski

We study the relation between viscosity solutions and weak solutions of the equation $\partial_{t} (∣ u ∣^{p - 2} u) = div (∣\nabla u ∣^{p - 2} \nabla u) .$ We pro…

math.AP2026

Entire $p$ -harmonic functions with an isolated critical point and failure of $C^{1}$ -regularity of the natural gradient

Erno Kauranen, Jarkko Siltakoski

For every $n \geq 2$ and $1 < p < \infty$ , we show an existence of a nonconstant homogeneous entire $p$ -harmonic function whose only critical point is the origin. The angular parts of the…

math.AP2026

Higher integrability for parabolic double phase equations with an improved gap bound

Abhrojyoti Sen, Jarkko Siltakoski

We prove a local higher integrability result for the gradient of Hölder continuous weak solutions to the parabolic double phase equation \[ \partial_t u - \operatorname{div} \left(…

math.AP2025

Lipschitz regularity for parabolic double phase equations with gradient nonlinearity

Abhrojyoti Sen, Jarkko Siltakoski

We establish the local Lipschitz regularity in space for the viscosity solutions to the parabolic double phase equation of the form \[ \smash{\partial_{t}u-\operatorname{div} \left…

math.AP2025

Existence of variational solutions to doubly nonlinear systems in general noncylindrical domains

Leah Schätzler, Christoph Scheven, Jarkko Siltakoski +1

We consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form \begin{align*} \partial_t \big( |u|^{q-1}u \big) - \operatorname{div} \big( D_ξf(x,u,Du) \big) = -…

math.AP2025★ 1 cited

Existence of variational solutions to doubly nonlinear systems in nondecreasing domains

Leah Schätzler, Christoph Scheven, Jarkko Siltakoski +1

For $q \in (0, \infty)$ , we consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form \begin{align*} \partial_t \big( |u|^{q-1}u \big) - \operatorname{div} \big…

math.AP2025

Lipschitz continuity and equivalence of positive viscosity and weak solutions to Trudinger's equation

Peter Lindqvist, Mikko Parviainen, Jarkko Siltakoski

We show that stricty positive viscosity supersolutions to Trudinger's equation are local weak supersolutions when $1 < p < \infty$ . As an application, we show using the Ishii-Lions met…

math.AP2023★ 1 cited

Intrinsic Harnack's inequality for a general nonlinear parabolic equation in non-divergence form

Tapio Kurkinen, Jarkko Siltakoski

We prove the intrinsic Harnack's inequality for a general form of a parabolic equation that generalizes both the standard parabolic $p$ -Laplace equation and the normalized version…

math.AP2022

The bounded slope condition for parabolic equations with time-dependent integrands

Leah Schätzler, Jarkko Siltakoski

In this paper, we study the Cauchy-Dirichlet problem \begin{equation*} \left\{ \begin{array}{ll} \mbox{ $\partial_{t} u - div (D_{ξ} f (t, D u)) = 0$ } & \mbox{i…

math.AP2022★ 3 cited

Elliptic Harnack's inequality for a singular nonlinear parabolic equation in non-divergence form

Tapio Kurkinen, Mikko Parviainen, Jarkko Siltakoski

We prove an elliptic Harnack's inequality for a general form of a parabolic equation that generalizes both the standard parabolic $p$ -Laplace equation and the normalized version th…

math.AP2021

Hölder gradient regularity for the inhomogeneous normalized $p (x)$ -Laplace equation

Jarkko Siltakoski

We prove the local gradient Hölder regularity of viscosity solutions to the inhomogeneous normalized $p (x)$ -Laplace equation $$ -Δu-(p(x)-2)\frac{\left\langle D^{2}uDu,Du\right\ran…

math.AP2020

Recovering a variable exponent

Tommi Brander, Jarkko Siltakoski

We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p (x)$ -Laplace equation from the Dirichlet-to-Neumann map. The variable expo…

math.AP2019

Equivalence between radial solutions of different non-homogeneous $p$ -Laplacian type equations

Jarkko Siltakoski

We study radial viscosity solutions to the equation \[ -\ |Du\ |^{q-2}Δ_{p}^{N}u=f(\ |x\ |)\quad\text{in }B_{R}\subset\mathbb{R}^{N}, \] where $f \in C [0, R)$ , $p, q \in (1, \infty)$ and…

math.AP2019

Equivalence of viscosity and weak solutions for a $p$ -parabolic equation

Jarkko Siltakoski

We study the relationship of viscosity and weak solutions to the equation \[ \smash{\partial_{t}u-Δ_{p}u=f(Du)} \] where $p > 1$ and $f \in C (R^{N})$ satisfies suitable assum…

math.AP2017

Equivalence of viscosity and weak solutions for the normalized $p (x)$ -Laplacian

Jarkko Siltakoski

We show that viscosity solutions to the normalized $p (x)$ -Laplace equation coincide with distributional weak solutions to the strong $p (x)$ -Laplace equation when $p$ is Lipschitz a…

Nonnegative Viscosity and Weak Solutions to Trudinger's Parabolic Equation

Entire p-harmonic functions with an isolated critical point and failure of C1-regularity of the natural gradient

Higher integrability for parabolic double phase equations with an improved gap bound

Lipschitz regularity for parabolic double phase equations with gradient nonlinearity

Existence of variational solutions to doubly nonlinear systems in general noncylindrical domains

Existence of variational solutions to doubly nonlinear systems in nondecreasing domains

Lipschitz continuity and equivalence of positive viscosity and weak solutions to Trudinger's equation

Intrinsic Harnack's inequality for a general nonlinear parabolic equation in non-divergence form

The bounded slope condition for parabolic equations with time-dependent integrands

Elliptic Harnack's inequality for a singular nonlinear parabolic equation in non-divergence form

Hölder gradient regularity for the inhomogeneous normalized p(x)-Laplace equation

Recovering a variable exponent

Equivalence between radial solutions of different non-homogeneous p-Laplacian type equations

Equivalence of viscosity and weak solutions for a p-parabolic equation

Equivalence of viscosity and weak solutions for the normalized p(x)-Laplacian

Entire $p$ -harmonic functions with an isolated critical point and failure of $C^{1}$ -regularity of the natural gradient

Hölder gradient regularity for the inhomogeneous normalized $p (x)$ -Laplace equation

Equivalence between radial solutions of different non-homogeneous $p$ -Laplacian type equations

Equivalence of viscosity and weak solutions for a $p$ -parabolic equation

Equivalence of viscosity and weak solutions for the normalized $p (x)$ -Laplacian