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Tapio Kurkinen

Publications and source records attributed to Tapio Kurkinen.

4 recordsLinked to original sources
arXiv2026

Quantitative stability for quasilinear parabolic equations

We examine the stability of a class of quasilinear parabolic partial differential equations under perturbations. We are interested in the behavior of viscosity solutions as the perturbation parameter vanishes and establish explicit convergence rates by adapting standard comparison arguments. Despite the possible singular or degenerate nature of the parabolic operator, our framework covers, in particular, both the normalized and the variational $p$-parabolic equations, providing quantitative estimates for perturbations of the exponent $p$ and limits arising from regularized approximations.

math.AP↗
arXiv2024

Boundary regularity for a general nonlinear parabolic equation in non-divergence form

We characterize regular boundary points in terms of a barrier family for a general form of a parabolic equation that generalizes both the standard parabolic $p$-Laplace equation and the normalized version arising from stochastic game theory. Using this result we prove geometric conditions that ensure regularity by constructing suitable barrier families. We also prove that when $q<2$, a single barrier does not suffice to guarantee regularity.

math.AP↗
arXiv2022

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

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 that has been proposed in stochastic game theory. This version of the inequality doesn't require the intrinsic waiting time and we get the estimate with the same time level on both sides of the inequality.

math.AP↗