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Homogenization of some viscous Hamilton--Jacobi equations using variational arguments on probability spaces — arXiv:2610.05423

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.05423
License (as archived): CC0-1.0
Archived: 2026-10-06T13:49:22.814Z
SHA-256 of the archived text: 0753911eccf3c34ed055522a5c881a83a482879a29a4be3dcd94154acc4f3207
Stable URL of this page: https://metraipolis.com/documento/dc_dc64bc8dcebf

How to cite

Homogenization of some viscous Hamilton--Jacobi equations using variational arguments on probability spaces — arXiv:2610.05423 — arXiv (en), https://arxiv.org/abs/2610.05423 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dc64bc8dcebf (Metraipolis archive dc_dc64bc8dcebf, sha256 0753911eccf3c34ed055522a5c881a83a482879a29a4be3dcd94154acc4f3207)

BibTeX

@misc{dcdc64bc8dcebf,
  title = {Homogenization of some viscous Hamilton--Jacobi equations using variational arguments on probability spaces — arXiv:2610.05423},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.05423},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dc64bc8dcebf; sha256 0753911eccf3c34ed055522a5c881a83a482879a29a4be3dcd94154acc4f3207},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.05423. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This work studies the asymptotic behavior of a class of viscous Hamilton--Jacobi equations with oscillatory periodic potentials, already studied by other authors in the PDE framework, and described in terms of an effective Hamiltonian. A novel variational approach is introduced, based on the classical stochastic control representation involving a Brownian motion, which allows the problem to be reformulated in terms of functionals defined on probability spaces. The core result is the identification of a homogenized Lagrangian obtained via a $\Gamma$-convergence procedure adapted to random processes, where filtrations and Brownian motions are treated as variables. The effective Hamiltonian is then recovered as the Legendre transform of this homogenized Lagrangian. The analysis provides both lower and upper bounds by means of blow-up arguments and the construction of stochastic correctors, yielding a complete characterization of the homogenized limit. This approach allows for a stability result with respect to the addition of some localized defects embedded in the periodic background.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Analysis of PDEs (math.AP) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2610.05423 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-06T12:06:32.225Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).