Erik Lindgren

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math.AP2025

Higher Hölder regularity for fractional $(p, q)$ -Laplace equations

Prashanta Garain, Erik Lindgren

We study the fractional $(p, q)$ -Laplace equation $(- Δ_{p})^{s} u + (- Δ_{q})^{t} u = 0$ for $s, t \in (0, 1)$ and $p, q \in (1, \infty)$ . We establish Hölder estimates with an explicit exponent.…

math.AP2024

Moving gradient singularity for the evolutionary $p$ -Laplace equation

Erik Lindgren, Jin Takahashi

We consider the evolutionary $p$ -Laplace equation in $R^{n}$ . For $p > n$ , we construct a solution $u$ with a moving gradient singularity in the sense that $|\nabla u(x,t)|\to…

math.AP2024

Higher Hölder regularity for a subquadratic nonlocal parabolic equation

Prashanta Garain, Erik Lindgren, Alireza Tavakoli

In this paper, we are concerned with the Hölder regularity for solutions of the nonlocal evolutionary equation $\partial_{t} u + (- Δ_{p})^{s} u = 0.$ Here, $(- Δ_{p})^{s}$ is the fractional…

Higher Hölder regularity for fractional (p,q)-Laplace equations

Moving gradient singularity for the evolutionary p-Laplace equation

Higher Hölder regularity for a subquadratic nonlocal parabolic equation

Higher Hölder regularity for fractional $(p, q)$ -Laplace equations

Moving gradient singularity for the evolutionary $p$ -Laplace equation