Global Compactness, Subcritical Approximation of the Sobolev Quotient, and a Related Concentration Result in the Heisenberg Group

Palatucci, Giampiero; Piccinini, Mirco; Temperini, Letizia

doi:10.1007/978-3-031-48579-4_15

Trends in Mathematics

2024

DOI: 10.1007/978-3-031-48579-4_15

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Global Compactness, Subcritical Approximation of the Sobolev Quotient, and a Related Concentration Result in the Heisenberg Group

Giampiero Palatucci,

Mirco Piccinini,

Letizia Temperini

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2024

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Struwe’s global compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group

Palatucci,

Piccinini,

Temperini

2024

Advances in Calculus of Variations

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We investigate some of the effects of the lack of compactness in the critical Folland–Stein–Sobolev embedding in very general (possible non-smooth) domains, by proving via De Giorgi’s Γ-convergence techniques that optimal functions for a natural subcritical approximations of the Sobolev quotient concentrate energy at one point. In the second part of the paper, we try to restore the compactness by extending the celebrated Global Compactness result to the Heisenberg group via a completely different approach with respect to the original one by Struwe [M. Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z. 187 1984, 4, 511–517].

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Struwe’s global compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group

Palatucci,

Piccinini,

Temperini

2024

Advances in Calculus of Variations

View full text Add to dashboard Cite

show abstract

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Global Compactness, Subcritical Approximation of the Sobolev Quotient, and a Related Concentration Result in the Heisenberg Group

Cited by 1 publication

References 18 publications

Struwe’s global compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group

Struwe’s global compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group

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