A Global Compactness type result for Palais-Smale sequences in fractional Sobolev spaces

By Giampiero Palatucci, A. Pisante. 2014

74 citations recorded by the source corpus.

We extend the Global Compactness result by M. Struwe (Math. Z, 1984) to any fractional Sobolev spaces $\dot{H}^s(\Omega)$ for $0<s<N/2$ and $\Omega \subset \mathbb{R}^N$ a bounded domain with smooth boundary. The proof is a simple direct consequence of the so-called Profile Decomposition of P. Gerard (ESAIM: Control, Optimisation and Calculus of Variations, 1998).

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/383260d5aaa8e088a0c7c653d8f9fc0c3729e30f

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In Applied Mathematics

1. Jihoon Ok
2. Giuseppe Mingione
3. Sun-Sig Byun
4. Giampiero Palatucci
5. Janne Korvenpää
6. Tuomo Kuusi
7. Cristiana De Filippis
8. Kyeong Song

In Computational Mechanics

1. Tuomo Kuusi
2. Janne Korvenpää
3. Giampiero Palatucci
4. Jihoon Ok

In Computational Theory and Mathematics

1. Jihoon Ok
2. Giuseppe Mingione
3. Giampiero Palatucci
4. Janne Korvenpää
5. Sun-Sig Byun
6. Tuomo Kuusi
7. Kyeong Song
8. Cristiana De Filippis

Citations in the corpus

• Hölder regularity for weak solutions to nonlocal double phase problems (2021, background): “We refer to, for instance, [7, 25, 26, 31, 39, 40, 41, 42, 44] for regularity results for nonlocal linear equations with fractional orders.”
• The obstacle problem for nonlinear integro-differential operators (2016, background): “the pseudo-di↵erential commutator approach in [34,35], cannot be plainly applied and seem di cult to adapt to the nonlinear framework considered here (mainly due to the non-Hilbertian nature of the involved fractional Sobolev spaces W s,p).”