Compensation phenomena for concentration effects via nonlinear elliptic estimates
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866917594526646272 |
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| author | Guerra, André Raiţă, Bogdan Schrecker, Matthew |
| author_facet | Guerra, André Raiţă, Bogdan Schrecker, Matthew |
| contents | We study compensation phenomena for fields satisfying both a pointwise and a linear differential constraint. This effect takes the form of nonlinear elliptic estimates, where constraining the values of the field to lie in a cone compensates for the lack of ellipticity of the differential operator. We give a series of new examples of this phenomenon for a geometric class of cones and operators such as the divergence or the curl. One of our main findings is that the maximal gain of integrability is tied to both the differential operator and the cone, contradicting in particular a recent conjecture from arXiv:2106.03077. This extends the recent theory of compensated integrability due to D. Serre. In particular, we find a new family of integrands that are Div-quasiconcave under convex constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_10657 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Compensation phenomena for concentration effects via nonlinear elliptic estimates Guerra, André Raiţă, Bogdan Schrecker, Matthew Analysis of PDEs Functional Analysis We study compensation phenomena for fields satisfying both a pointwise and a linear differential constraint. This effect takes the form of nonlinear elliptic estimates, where constraining the values of the field to lie in a cone compensates for the lack of ellipticity of the differential operator. We give a series of new examples of this phenomenon for a geometric class of cones and operators such as the divergence or the curl. One of our main findings is that the maximal gain of integrability is tied to both the differential operator and the cone, contradicting in particular a recent conjecture from arXiv:2106.03077. This extends the recent theory of compensated integrability due to D. Serre. In particular, we find a new family of integrands that are Div-quasiconcave under convex constraints. |
| title | Compensation phenomena for concentration effects via nonlinear elliptic estimates |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2112.10657 |