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

Tapio Kurkinen; Jarkko Siltakoski

doi:10.1007/s11118-024-10141-9

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

Analysis of PDEs 2025-06-23 v3

Authors: Tapio Kurkinen , Jarkko Siltakoski

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Abstract

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 arising from stochastic game theory. We prove each result for the optimal range of exponents and ensure that we get stable constants.

Keywords

intrinsic harnack inequality nonlinear parabolic equation non-divergence form p-laplace equation stochastic game theory optimal exponents

Cite

@article{arxiv.2308.13443,
  title  = {Intrinsic Harnack's inequality for a general nonlinear parabolic equation in non-divergence form},
  author = {Tapio Kurkinen and Jarkko Siltakoski},
  journal= {arXiv preprint arXiv:2308.13443},
  year   = {2025}
}

Comments

52 pages. The revision corrects a scaling mistake in the proof of Theorem 4.1. by adding Corollary 2.5. The results remain unchanged

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