{"paper":{"title":"A priori estimates and large population limits for some nonsymmetric Nash systems with semimonotonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Davide Francesco Redaelli, Marco Cirant","submitted_at":"2024-06-16T07:18:00Z","abstract_excerpt":"We address the problem of regularity of solutions $u^i(t, x^1, \\dots, x^N)$ to a family of semilinear parabolic systems of $N$ equations, which describe closed-loop equilibria of some $N$-player differential games with Lagrangian having quadratic behaviour in the velocity variable, running costs $f^i(x)$ and final costs $g^i(x)$. By global (semi)monotonicity assumptions on the data $f=(f^i)_{1 \\leq i \\leq N}$ and $g=(g^i)_{1 \\leq i \\leq N}$, and assuming that derivatives of $f^i, g^i$ in directions $x^j$ are of order $1/N$ for $j \\neq i$, we prove that derivatives of $u^i$ enjoy the same prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.10822","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.10822/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}