{"paper":{"title":"A sharp $L_p$-regularity result for second-order stochastic partial differential equations with unbounded and fully degenerate leading coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ildoo Kim, Kyeong-Hun Kim","submitted_at":"2019-05-18T07:29:14Z","abstract_excerpt":"We present existence, uniqueness, and sharp regularity results of solution\n  to the stochastic partial differential equation (SPDE)\n  \\begin{align}\n  \\label{abs eqn}\n  du=(a^{ij}(\\omega,t)u_{x^ix^j}+f)dt + (\\sigma^{ik}(\\omega,t)u_{x^i}+g^k)dw^k_t, \\quad u(0,x)=u_0,\n  \\end{align}\n  where $\\{w^k_t:k=1,2,\\cdots\\}$ is a sequence of independent Brownian motions. The coefficients are merely measurable in $(\\omega,t)$ and can be unbounded and fully degenerate, that is, coefficients $a^{ij}$, $\\sigma^{ik}$ merely satisfy\n  \\begin{align}\n  \\label{abs only} \\left(\\alpha^{ij}(\\omega,t)\\right)_{d\\times d}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07545","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"}