Abstract
We study subsolutions for semilinear elliptic boundary value problems in L1. We consider as well nonlinear as linear boundary conditions. The nonlinear functions may be multivated. We characterize in terms of p.d.e. the subsolutions defined by a nonlinear functional analysis argument. Applications are given to obtain existence results for semilinear elliptic boundary value problems and comparison and estimates for nonlinear parabolic boundary value problems.
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Benilan, P., Boulaamayel, B. Sous-solutions d'équations elliptiques dans L1. Potential Analysis 10, 215–241 (1999). https://doi.org/10.1023/A:1008684818001
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DOI: https://doi.org/10.1023/A:1008684818001