Nonnegative Viscosity and Weak Solutions to Trudinger's Parabolic Equation

Abstract

We study the relation between viscosity solutions and weak solutions of the equation ∂_t(|u|^p−2u) = div(|∇ u|^p−2∇ u). We prove that at least for non-negative functions these are equivalent concepts.

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BibTeX RIS

BibTeX

@misc{lindqvist2026nonnegative,
  title = {{Nonnegative Viscosity and Weak Solutions to Trudinger's Parabolic Equation}},
  author = {Peter Lindqvist and Mikko Parviainen and Jarkko Siltakoski},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09905},
  eprint = {2610.09905},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09905},
}

RIS

TY  - UNPB
TI  - Nonnegative Viscosity and Weak Solutions to Trudinger's Parabolic Equation
AU  - Peter Lindqvist
AU  - Mikko Parviainen
AU  - Jarkko Siltakoski
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09905
UR  - https://arxiv.org/abs/2610.09905
AB  - We study the relation between viscosity solutions and weak solutions of the equation ∂_t(|u|^p−2u) = div(|∇ u|^p−2∇ u). We prove that at least for non-negative functions these are equivalent concepts.
ER  -

Abstract

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