Improvement of flatness for nonlocal phase transitions

We prove an improvement of flatness result for nonlocal phase transitions. For a class of nonlocal equations, we obtain a result in the same spirit of a celebrated theorem of Savin for the classical case. The results presented are completely new even for the case of the fractional Laplacian, but the robustness of the proofs allows us to treat also more general, possibly anisotropic, integro-differential operators.

Keywords

Nonlocal phase transitions, rigidity results, sliding methods

URI

https://doi.org/10.34657/2522
https://oa.tib.eu/renate/handle/123456789/2253

Citation

Dipierro, S., Serra, J., & Valdinoci, E. (2016). Improvement of flatness for nonlocal phase transitions (Vol. 2345). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2345

Collections

Mathematik

License

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