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Alessio
Figalli
false
en
1-32
In this paper we prove optimal regularity for the convex envelope of supersolutions to general fully nonlinear elliptic equations with unbounded coefficients. More precisely, we deal with coefficients and right hand sides (RHS) in Lq with q≥n. This extends the result of Caffarelli on the Cloc1,1 regularity of the convex envelope of supersolutions of fully nonlinear elliptic equations with bounded RHS. Moreover, we also provide a regularity result with estimates for ω-semiconvex functions that are supersolutions to the same type of equations with unbounded RHS (i.e, RHS in Lq,q≥n). By a completely different method, our results here extend the recent regularity results obtained by Braga et al. (Adv Math 334:184–242, 2018) for q>n, as far as fully nonlinear PDEs are concerned. These results include, in particular, the apriori estimate obtained by Caffarelli et al. (Commun Pure Appl Math 38(2):209–252, 1985) on the modulus of continuity of the gradient of ω-semiconvex supersolutions (for linear equations and bounded RHS) that have a Hölder modulus of semiconvexity.
https://link.springer.com/10.1007%2Fs00220-019-03370-2
2019-04
Optimal Regularity for the Convex Envelope and Semiconvex Functions Related to Supersolutions of Fully Nonlinear Elliptic Equations
articles
https://scigraph.springernature.com/explorer/license/
2019-04-01
2019-04-11T13:31
research_article
1
1432-0916
0010-3616
Communications in Mathematical Physics
doi
10.1007/s00220-019-03370-2
readcube_id
2be283904c0c5fb9880129c80aaa3836cd9ceabc07a5b89dc5c686238f439967
J. Ederson M.
Braga
Applied Mathematics
pub.1112964839
dimensions_id
Springer Nature - SN SciGraph project
Universidade Federal do Ceará
Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici - Bloco 914, CEP 60455-760, Fortaleza, Ceará, Brazil
Department of Mathematics, ETH Zürich, HG G 63.2, Rämistrasse 101, 8092, Zürich, Switzerland
Swiss Federal Institute of Technology in Zurich
Mathematical Sciences
Moreira
Diego