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A Brezis-Nirenberg type result for mixed local and nonlocal operators

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arxiv 2209.07502 v2 pith:F3K6QSKH submitted 2022-09-15 math.AP

Stefano Biagi , Serena Dipierro , Enrico Valdinoci , Eugenio Vecchi This is my paper · ORCID
classification math.AP
keywords correspondinglaplacianmixedproblemachievedbrezis-nirenbergconstantcritical
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We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding Sobolev inequality, detecting the optimal constant, which we show that is never achieved. Moreover, we present an existence (and nonexistence) theory for the corresponding subcritical perturbation problem.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Regularity results for a class of mixed local and nonlocal singular problems involving distance function

    math.AP 2024-11 conditional novelty 6.0 of 10

    For mixed local-nonlocal singular quasilinear elliptic problems, the authors establish existence, uniqueness under a boundary-weight restriction, sharp Sobolev regularity, boundary behavior, and Hölder regularity with...

  2. Multiplicity result for mixed local and nonlocal Kirchhoff problem involving critical growth

    math.AP 2024-11 reject novelty 4.0 of 10

    The paper claims two nonnegative solutions for a mixed local/nonlocal Kirchhoff equation with critical growth and sign-changing weight, but the proof has notable gaps.

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