Saara Sarsa

activity

20202025

most citedNote on an elementary inequality and its application to the regularity of

p

-harmonic functions

1 citations · 2 across the 7 of their papers we have counts for

collaborators

8 papers

math.AP2025

Trudinger's Parabolic Equation

Peter Lindqvist, Mikko Parviainen, Saara Sarsa

We study the uniqueness of non-negative solutions of the equation \begin{align*} \partial_t\left(|u|^{p-2}u\right)\,=\, \operatorname{div}(|\nabla u|^{p-2}\nabla u). \end{align*} B…

math.MG2025

Duality for the gradient of a $p$ -harmonic function and the existence of gradient curves

Sylvester Eriksson-Bique, Saara Sarsa

Every convex optimization problem has a dual problem. The $p$ -Dirichlet problem in metric measure spaces is an optimization problem whose solutions are $p$ -harmonic functions. What…

math.AP2024

Second order Sobolev regularity results for the generalized $p$ -parabolic equation

Yawen Feng, Mikko Parviainen, Saara Sarsa

We study a general class of parabolic equations $u_{t} - ∣ D u ∣^{γ} (Δ u + (p - 2) Δ_{\infty}^{N} u) = 0,$ which can be highly degenerate or singular. This class contains as special cases…

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

A systematic approach on the second order regularity of solutions to the general parabolic $p$ -Laplace equation

Yawen Feng, Mikko Parviainen, Saara Sarsa

We study a general form of a degenerate or singular parabolic equation $u_{t} - ∣ D u ∣^{γ} (Δ u + (p - 2) Δ_{\infty}^{N} u) = 0$ that generalizes both the standard parabolic $p$ -Laplace equa…

math.AP2022

Global second order Sobolev-regularity of $p$ -harmonic functions

Akseli Haarala, Saara Sarsa

We prove a global version of the classical result that $p$ -harmonic functions belong to $W_{l oc}^{2, 2}$ for $1 < p < 3 + \frac{2}{n - 2}$ . The proof relies on Cordes' matrix inequalities […

math.AP2021★ 1 cited

On the second order regularity of solutions to the parabolic $p$ -Laplace equation

Yawen Feng, Mikko Parviainen, Saara Sarsa

In this paper, we study the second order Sobolev regularity of solutions to the parabolic $p$ -Laplace equation. For any $p$ -parabolic function $u$ , we show that $D(|Du|^{\frac{p-2+…

math.AP2020★ 1 cited

Note on an elementary inequality and its application to the regularity of $p$ -harmonic functions

Saara Sarsa

We study the Sobolev regularity of $p$ -harmonic functions. We show that $∣ D u ∣^{\frac{p - 2 + s}{2}} D u$ belongs to the Sobolev space $W_{l oc}^{1, 2}$ , $s > - 1 - \frac{p - 1}{n - 1}$ , for any $p$ …

Trudinger's Parabolic Equation

Duality for the gradient of a p-harmonic function and the existence of gradient curves

Second order Sobolev regularity results for the generalized p-parabolic equation

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

A systematic approach on the second order regularity of solutions to the general parabolic p-Laplace equation

Global second order Sobolev-regularity of p-harmonic functions

On the second order regularity of solutions to the parabolic p-Laplace equation

Note on an elementary inequality and its application to the regularity of p-harmonic functions

Duality for the gradient of a $p$ -harmonic function and the existence of gradient curves

Second order Sobolev regularity results for the generalized $p$ -parabolic equation

A systematic approach on the second order regularity of solutions to the general parabolic $p$ -Laplace equation

Global second order Sobolev-regularity of $p$ -harmonic functions

On the second order regularity of solutions to the parabolic $p$ -Laplace equation

Note on an elementary inequality and its application to the regularity of $p$ -harmonic functions