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Starshapedness of the superlevel sets of solutions to equations involving the fractional Laplacian in starshaped rings

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  • Sven Jarohs
  • Tadeusz Kulczycki
  • Paolo Salani

Abstract

We study solutions of the problem 0.1 −(−Δ)α/2u=f(x,u)inD0∖D¯1,u=0inRN∖D0,u=1inD¯1, where D1,D0⊂RN are open sets such that D¯1⊂D0, α∈(0,2), and f is a nonlinearity. Under different assumptions on f we prove that, if D0 and D1 are starshaped with respect to the same point x¯∈D¯1, then the same occurs for every superlevel set of u.

Suggested Citation

  • Sven Jarohs & Tadeusz Kulczycki & Paolo Salani, 2019. "Starshapedness of the superlevel sets of solutions to equations involving the fractional Laplacian in starshaped rings," Mathematische Nachrichten, Wiley Blackwell, vol. 292(5), pages 1008-1021, May.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:5:p:1008-1021
    DOI: 10.1002/mana.201700226
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