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pith:FU3TLJ4X

pith:2026:FU3TLJ4X43XO3CSLBUZKOZYIDY

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The evolution variational inequality for weighted Wasserstein metrics in non-convex bounded domains

Kyogo Murai

The weighted Wasserstein metric satisfies the evolution variational inequality in non-convex bounded domains.

arxiv:2605.13420 v1 · 2026-05-13 · math.AP

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Claims

C1strongest claim

we establish the evolution variational inequality for the weighted Wasserstein distance, without assuming convexity of domains... we apply the evolution variational inequality to the minimizing movement in weighted Wasserstein metrics to obtain weak solutions of Keller--Segel systems and Cahn--Hilliard type equations in non-convex domains.

C2weakest assumption

The boundary integral arising from the non-convexity can be controlled by Sobolev trace embedding and a variant of Kato's inequality and absorbed into the good terms of the energy dissipation inequality.

C3one line summary

The evolution variational inequality for weighted Wasserstein metrics holds on non-convex bounded domains by absorbing boundary integrals via Sobolev trace embeddings and a variant of Kato's inequality.

References

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[1] J. D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84 (2000), 375--393 2000

[2] H. Brezis and P. Mironescu, Gagliardo--Nirenberg inequalities and non-inequalities: the full story. Ann. Inst. H. Poincar\'e C Anal. Non Lin\'eaire 35 (2018), 1355--1376 2018

[3] J. W. Cahn and J. E. Hilliard, Spinodal decomposition: A reprise. Acta Metallurgica 19 (1961), 151–-161 1961

[4] J. A. Carrillo, S. Lisini, G. Savar\'e and D. Slep c ev, Nonlinear mobility continuity equations and generalized displacement convexity. J. Funct. Anal. 258 (2010), 1273--1309 2010

[5] J. Dolbeault, B. Nazaret and G. Savar\'e, A new class of transport distances between measures. Calc. Var. Partial Differential Equations 34 (2009), 193--231 2009

Receipt and verification

First computed	2026-05-18T02:44:47.341363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d3735a797e6eeed8a4b0d32a767081e09cfbe642917a685eee8e3de6cbe6f2e

Aliases

arxiv: 2605.13420 · arxiv_version: 2605.13420v1 · doi: 10.48550/arxiv.2605.13420 · pith_short_12: FU3TLJ4X43XO · pith_short_16: FU3TLJ4X43XO3CSL · pith_short_8: FU3TLJ4X

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FU3TLJ4X43XO3CSLBUZKOZYIDY \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2d3735a797e6eeed8a4b0d32a767081e09cfbe642917a685eee8e3de6cbe6f2e

Canonical record JSON

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    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T12:14:36Z",
    "title_canon_sha256": "997f64db0538f6b9c5da1e8215da0f6e51263cb6813d636e1798b77bf84a6e8a"
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