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Variational maximum principle for elliptic systems involving the fractional Laplacian

  • Differential Equations and Dynamical Systems. Dedicated To Giorgio Fusco
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A Correction to this article was published on 11 July 2024

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Abstract

It is the aim of this note is to develop a maximum principle for elliptic systems involving the fractional Laplacian under minimal assumptions on the nonlinear term.

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Notes

  1. f defined like that is a Lipschitz function of Lipschitz constant \(Lip(f) \le 1\).

References

  1. Bucur, C., Valdinoci, E.: Nonlocal Diffusion and Applications, vol. 20. Springer, Berlin (2016)

    Google Scholar 

  2. Alikakos, N.D., Fusco, G., Smyrnelis, P.: Elliptic Systems of Phase Transition Type. PNLDE 91. Green Series, Birkhäuser, Basel (2018)

    Book  Google Scholar 

  3. Di Nezza, E., Palatucci, G., Valdinoci, E.: Hitchhiker’s guide to the fractional \(\text{ S }\)obolev spaces. Bull. Sci. Math. 136(5), 521–573 (2012)

    Article  MathSciNet  Google Scholar 

  4. Ros-Oton, X.: Nonlocal elliptic equations in bounded domains: a survey. Publ. Mat 60, 3–26 (2016)

    Article  MathSciNet  Google Scholar 

  5. Bisci, G.M., Radulescu, V.D., Servadei, R.: Variational Methods for Nonlocal Fractional Problems, vol. 162. Cambridge University Press, Cambridge (2016)

    Book  Google Scholar 

  6. Agranovich, M.S.: Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains. Springer, Berlin (2015)

    Book  Google Scholar 

  7. Brezis, H.: How to recognize constant functions: \(\text{ C }\)onnections with \( \text{ S }\)obolev spaces. Russ. Math. Surv. 57(4), 693 (2002)

    Article  MathSciNet  Google Scholar 

  8. Bourgain, J., Brezis, H., Mironescu, P.: Lifting in \({\rm s}\)obolev spaces. Journal d’Analyse Mathématique 80(1), 37 (2000)

    Article  MathSciNet  Google Scholar 

  9. Jarohs, S., Weth, T.: On the strong maximum principle for nonlocal operators. Math. Z. 293(1–2), 81–111 (2019)

    Article  MathSciNet  Google Scholar 

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Funding

NDA was supported by the National Recovery and Resilience Plan “Greece 2.0” funded by the European Union - NextGenerationEU (H.F.R.I. Project Number: 016097).

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Correspondence to N. D. Alikakos.

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Communicated by Carlos Rocha.

To Giorgio Fusco, original thinker, dear friend, lifelong collaborator and teacher.

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Alikakos, N.D., Nikolouzos, M. & Yannacopoulos, A.N. Variational maximum principle for elliptic systems involving the fractional Laplacian. São Paulo J. Math. Sci. (2024). https://doi.org/10.1007/s40863-024-00429-4

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  • DOI: https://doi.org/10.1007/s40863-024-00429-4

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