{"paper":{"title":"Regularity theory for general stable operators: parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xavier Fern\\'andez-Real, Xavier Ros-Oton","submitted_at":"2015-11-19T18:44:53Z","abstract_excerpt":"We establish sharp interior and boundary regularity estimates for solutions to $\\partial_t u - L u = f(t, x)$ in $I\\times \\Omega$, with $I \\subset \\mathbb{R}$ and $\\Omega \\subset\\mathbb{R}^n$. The operators $L$ we consider are infinitessimal generators of stable L\\'evy processes. These are linear nonlocal operators with kernels that may be very singular. On the one hand, we establish interior estimates, obtaining that $u$ is $C^{2s+\\alpha}$ in $x$ and $C^{1+\\frac{\\alpha}{2s}}$ in $t$, whenever $f$ is $C^{\\alpha}$ in $x$ and $C^{\\frac{\\alpha}{2s}}$ in $t$. In the case $f\\in L^\\infty$, we prove "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06301","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":""},"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"}