{"paper":{"title":"Maximum principles, extension problem and inversion for nonlocal one-sided equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA","math.PR"],"primary_cat":"math.AP","authors_text":"A. Bernardis, F. J. Mart\\'in-Reyes, J. L. Torrea, P. R. Stinga","submitted_at":"2015-05-12T16:04:26Z","abstract_excerpt":"We study one-sided nonlocal equations of the form $$\\int_{x_0}^\\infty\\frac{u(x)-u(x_0)}{(x-x_0)^{1+\\alpha}} dx=f(x_0),$$ on the real line. Notice that to compute this nonlocal operator of order $0<\\alpha<1$ at a point $x_0$ we need to know the values of $u(x)$ to the right of $x_0$, that is, for $x\\geq x_0$. We show that the operator above corresponds to a fractional power of a one-sided first order derivative. Maximum principles and a characterization with an extension problem in the spirit of Caffarelli--Silvestre and Stinga--Torrea are proved. It is also shown that these fractional equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03075","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"}