TY - JOUR
T1 - Regularity of solutions in semilinear elliptic theory
AU - Indrei, Emanuel
AU - Minne, Andreas
AU - Nurbekyan, Levon
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank Henrik Shahgholian for introducing us to the regularity problem for semilinear equations. Special thanks go to John Andersson for valuable feedback on a preliminary version of the paper. E. Indrei acknowledges: (i) support from NSF Grants OISE-0967140 (PIRE), DMS-0405343, and DMS-0635983 administered by the Center for Nonlinear Analysis at Carnegie Mellon University and an AMS-Simons Travel Grant; (ii) the hospitality of the Max Planck Institute in Leipzig and University of Oxford where part of the research was carried out. L. Nurbekyan was partially supported by KAUST baseline and start-up funds and KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering.
PY - 2016/7/8
Y1 - 2016/7/8
N2 - We study the semilinear Poisson equation
Δu=f(x,u)inB1.
(1)
Our main results provide conditions on f which ensure that weak solutions of (1) belong to C1,1(B1/2). In some configurations, the conditions are sharp.
AB - We study the semilinear Poisson equation
Δu=f(x,u)inB1.
(1)
Our main results provide conditions on f which ensure that weak solutions of (1) belong to C1,1(B1/2). In some configurations, the conditions are sharp.
UR - http://hdl.handle.net/10754/617289
UR - http://link.springer.com/10.1007/s13373-016-0088-z
UR - http://www.scopus.com/inward/record.url?scp=85015965332&partnerID=8YFLogxK
U2 - 10.1007/s13373-016-0088-z
DO - 10.1007/s13373-016-0088-z
M3 - Article
SN - 1664-3607
VL - 7
SP - 177
EP - 200
JO - Bulletin of Mathematical Sciences
JF - Bulletin of Mathematical Sciences
IS - 1
ER -