{"paper":{"title":"Approximate homogenization of convex nonlinear elliptic PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adam M. Oberman, Chris Finlay","submitted_at":"2017-10-27T19:35:54Z","abstract_excerpt":"We approximate the homogenization of fully nonlinear, convex, uniformly elliptic Partial Differential Equations in the periodic setting, using a variational formula for the optimal invariant measure, which may be derived via Legendre-Fenchel duality. The variational formula expresses $\\bar H$ as an average of the operator against the optimal invariant measure, generalizing the linear case. Several nontrivial analytic formulas for $\\bar H$ are obtained. These formulas are compared to numerical simulations, using both PDE and variational methods. We also perform a numerical study of convergence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10309","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}