Abstract
In this paper we give a new, less restrictive condition for removability of singular sets, E, of smooth solutions to the m-Hessian equation (and also for more general fully nonlinear elliptic equations) in \(\Omega {\setminus } E\), \(\Omega \subset \mathbb R^n\). Besides the existence and regularity results for these equations, the proof only makes use of the classical elliptic theory, i.e. the classical maximum principles and a Hopf lemma.
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Acknowledgements
The first author wants to thank her advisor Friedmar Schulz for suggesting the topic, giving helpful remarks and pointing out the references [10, 11, 15, 17] to her. This paper will be part of the PhD thesis of the first author. We also thank Anna Dall’Acqua for carefully reading through the paper and providing us with valuable advice and helpful comments.
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Car, H., Pröpper, R. Removable singularities of \(\varvec{m}\)-Hessian equations. Nonlinear Differ. Equ. Appl. 24, 6 (2017). https://doi.org/10.1007/s00030-016-0429-3
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DOI: https://doi.org/10.1007/s00030-016-0429-3