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    Regularity of solutions in semilinear elliptic theory

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    art3A10.10072Fs13373-016-0088-z.pdf
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    Type
    Article
    Authors
    Indrei, Emanuel
    Minne, Andreas
    Nurbekyan, Levon cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2016-07-08
    Online Publication Date
    2016-07-08
    Print Publication Date
    2017-04
    Permanent link to this record
    http://hdl.handle.net/10754/617289
    
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    Abstract
    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 Sciences
    Sponsors
    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
    Springer Nature
    Journal
    Bulletin of Mathematical Sciences
    DOI
    10.1007/s13373-016-0088-z
    arXiv
    arXiv:1601.05219
    Additional Links
    http://link.springer.com/10.1007/s13373-016-0088-z
    ae974a485f413a2113503eed53cd6c53
    10.1007/s13373-016-0088-z
    Scopus Count
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    Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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