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Recently this problem was studied in the \"coercive\" case $\\lambda c\\le0$, where uniqueness of solutions can be expected, and it was conjectured that the solution set is more complex for noncoercive equations. This conjecture w"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.01661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-05T20:51:36Z","cross_cats_sorted":[],"title_canon_sha256":"8e421be61e0709a283d1c0049fbade27d7425be5a3bafba5b163ea2740bca945","abstract_canon_sha256":"406dc1b06198ccecddea8bd5a39e562da22b798a92fef98f6887681ce694153c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:38.668608Z","signature_b64":"RplLQVw0pC9IiUUJs5jMSHynzDFj/k7m94/GOve+TTQF+9UjgJh4gUCCMgQCpcyxYAYoQ1XoJ+ttGLPvxBcoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d40af44e1ab82e880af012dd3112a360648bdcc0b8007815b47714f536cc7120","last_reissued_at":"2026-05-18T00:21:38.667860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:38.667860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A priori bounds and multiplicity for fully nonlinear equations with quadratic growth in the gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Boyan Sirakov, Gabrielle Nornberg","submitted_at":"2018-02-05T20:51:36Z","abstract_excerpt":"We consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient, such as $$ -F(x,u,Du,D^2u) =\\lambda c(x)u+\\langle M(x)D u, D u \\rangle +h(x) $$ in a bounded domain with a Dirichlet boundary condition, here $\\lambda \\in\\mathbb{R}$, $c,\\, h \\in L^p(\\Omega)$, $p>n\\geq 1$, $c\\gneqq 0$ and the matrix $M$ satisfies $0<\\mu_1 I\\leq M\\leq \\mu_2 I$. Recently this problem was studied in the \"coercive\" case $\\lambda c\\le0$, where uniqueness of solutions can be expected, and it was conjectured that the solution set is more complex for noncoercive equations. 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