{"paper":{"title":"Fractional differentiability for solutions of nonlinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Albert Clop, Antonia Passarelli di Napoli, Antonio L. Bais\\'on, Joan Orobitg, Raffaella Giova","submitted_at":"2016-03-17T16:27:07Z","abstract_excerpt":"We study nonlinear elliptic equations in divergence form $${\\operatorname{div}}{\\mathcal A}(x,Du)={\\operatorname{div}}G.$$ When ${\\mathcal A}$ has linear growth in $Du$, and assuming that $x\\mapsto{\\mathcal A}(x,\\xi)$ enjoys $B^\\alpha_{\\frac{n}\\alpha, q}$ smoothness, local well-posedness is found in $B^\\alpha_{p,q}$ for certain values of $p\\in[2,\\frac{n}{\\alpha})$ and $q\\in[1,\\infty]$. In the particular case ${\\mathcal A}(x,\\xi)=A(x)\\xi$, $G=0$ and $A\\in B^\\alpha_{\\frac{n}\\alpha,q}$, $1\\leq q\\leq\\infty$, we obtain $Du\\in B^\\alpha_{p,q}$ for each $p<\\frac{n}\\alpha$. Our main tool in the proof i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05565","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"}