Effect of the Domain Geometry on the Solutions to Fractional Brezis-Nirenberg Problem
In this paper, we consider the Brezis-Nirenberg problem for the nonlocal fractional elliptic equation Aαux=NN-2αuxp+εux, x∈Ω, ux>0, x∈Ω, u(x)=0, x∈∂Ω, where 0<α<1 is fixed, p=N+2α/N-2α, ε is a small parameter, and Ω is a bounded smooth domain of RN(N≥4α). Aα denotes the fractional Laplace o...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/1093804 |
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| Summary: | In this paper, we consider the Brezis-Nirenberg problem for the nonlocal fractional elliptic equation Aαux=NN-2αuxp+εux, x∈Ω, ux>0, x∈Ω, u(x)=0, x∈∂Ω, where 0<α<1 is fixed, p=N+2α/N-2α, ε is a small parameter, and Ω is a bounded smooth domain of RN(N≥4α). Aα denotes the fractional Laplace operator defined through the spectral decomposition. Under some geometry hypothesis on the domain Ω, we show that all solutions to this problem are least energy solutions. |
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| ISSN: | 2314-8896 2314-8888 |