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2016-07-08Online Publication Date
2016-07-08Print Publication Date
2017-04Permanent link to this record
http://hdl.handle.net/10754/617289
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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.Citation
Regularity of solutions in semilinear elliptic theory 2016 Bulletin of Mathematical SciencesSponsors
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.Publisher
World Scientific Pub Co Pte LtarXiv
1601.05219Additional Links
http://link.springer.com/10.1007/s13373-016-0088-zae974a485f413a2113503eed53cd6c53
10.1007/s13373-016-0088-z