The CKN inequality for spinors: symmetry and symmetry breaking
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913806039384064 |
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| author | Dolbeault, Jean Esteban, Maria J. Frank, Rupert L. Loss, Michael |
| author_facet | Dolbeault, Jean Esteban, Maria J. Frank, Rupert L. Loss, Michael |
| contents | This paper is devoted to Sobolev interpolation inequalities for spinors, with weights of Caffarelli-Kohn-Nirenberg (CKN) type. In view of the corresponding results for scalar functions, a natural question is to determine whether optimal spinors have symmetry properties, or whether spinors with symmetry properties are linearly unstable, in which case we shall say that symmetry breaking occurs. What symmetry means has to be carefully defined and the overall picture turns out to be richer than in the scalar case. So far, no symmetrization technique is available in the spinorial case. We can however determine a range of the parameters for which symmetry holds using a detailed analysis based mostly on spectral methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_16909 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The CKN inequality for spinors: symmetry and symmetry breaking Dolbeault, Jean Esteban, Maria J. Frank, Rupert L. Loss, Michael Analysis of PDEs Functional Analysis 35B06, 26D10, 81Q10 This paper is devoted to Sobolev interpolation inequalities for spinors, with weights of Caffarelli-Kohn-Nirenberg (CKN) type. In view of the corresponding results for scalar functions, a natural question is to determine whether optimal spinors have symmetry properties, or whether spinors with symmetry properties are linearly unstable, in which case we shall say that symmetry breaking occurs. What symmetry means has to be carefully defined and the overall picture turns out to be richer than in the scalar case. So far, no symmetrization technique is available in the spinorial case. We can however determine a range of the parameters for which symmetry holds using a detailed analysis based mostly on spectral methods. |
| title | The CKN inequality for spinors: symmetry and symmetry breaking |
| topic | Analysis of PDEs Functional Analysis 35B06, 26D10, 81Q10 |
| url | https://arxiv.org/abs/2504.16909 |