Abstract
Our main result in this note can be stated as follows: Assume \(E\subset B_{1}\) and
holds in the \(C-\)viscosity sense where \(|E|=0\) and F is a degenerate elliptic operator. This way, (0.1) holds in the whole unit ball \(B_{1}\) (i.e, E is removable for (0.1)) provided
where \(f\in L^{n}(B_{1})\). Zeroth order term can appear in (0.2) provided u is bounded in \(B_{1}\). This extends a result due to Caffarelli et al. proven in (Commun Pure Appl Math 66(1):109–143, 2013) where a second order linear uniformly elliptic PDE with bounded RHS appeared in place of (0.2).
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Acknowledgements
The authors would like to thank Professor Yanyan Li for nice discussions about the topic treated in this paper. Also, the authors would like to thank both referees for careful reading and nice suggestions and comments on this paper. The first author is supported by CAPES-Brazil. The second author is partially supported by CNPq-Brazil.
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Braga, J.E.M., Moreira, D. Zero Lebesgue measure sets as removable sets for degenerate fully nonlinear elliptic PDEs. Nonlinear Differ. Equ. Appl. 25, 11 (2018). https://doi.org/10.1007/s00030-018-0499-5
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DOI: https://doi.org/10.1007/s00030-018-0499-5